PEACTICAL  LOGIC; 


OR,   THE 


AET  OF  THINKING. 


BY 


D.  S.  GREGORY,  D.D.. 

PRESIDENT  OF  LAKE  FOREST  UNIVERSITY. 


Of    THE 

UNIVERSITY 

or 


NEW  YORK  AND  PHILADELPHIA 

HINDS,  NOBLE  &  ELDREDGE 


WFFITT 


J^AX 


Entered,  according  to  Act  of  Congress,  in  the  year  1881,  by 

ELDREDGE  &  BROTHER, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


PREFACE. 


"VTEXT  to  right  and  noble  living,  which  is  the  highest  thing 
•U*  to  which  man  may  aspire,  may  be  placed  the  right  think- 
ing which  is  essential  to  such  living.  Logic,  as  the  Science 
of  the  Laws  of  Thought,  is  very  widely  studied,  in  the  higher 
schools,  as  an  aid  to  the  pupil  in  thinking ;  yet  it  is  the  set- 
tled conviction  of  many  of  the  best  educators  that  this  Sci- 
ence, as  it  is  ordinarily  presented,  does  very  little  toward 
training  to  think  or  preparing  for  thinking.  In  short,  there 
seems  to  be  a  growing  feeling  that  it  rather  serves,  in  case 
of  the  average  mind,  to  cram  the  memory  and  paralyze  the 
thinking  powers.  The  author  of  this  volume  shares  to  some 
extent  in  this  conviction  and  feeling;  hence  the  present 
attempt  to  construct  a  Practical  Logic,  by  the  use  of  which 
intelligent  teachers  may  train  inquiring  minds  to  correct 
thinking. 

The  only  way  to  learn  to  think  is  by  thinking;  the  only 
way  of  training  a  pupil  to  think  is  by  making  him  practise 
thinking.  Assuming  the  correctness  of  this  principle,  Logi- 
cal Praxis  is  made  the  prominent  and  essential  feature  of 
the  work.  Each  principle  of  thought  is  turned  into  a  Rule, 

iii 

215264 


IV  PREFACE. 

and  then  made  part  of  the  mental  property  and  power  of  the 
student  by  abundant  exercises. 

The  best  training  in  thinking  must  be  intelligent  and  sys- 
tematic. Accordingly  the  foundation  for  this  is  laid  by  a 
comprehensive  and  systematic  presentation  of  the  forms  and 
laws  of  thinking.  The  processes  of  formation  and  unfolding, 
of  involution  and  evolution,  are  presented  in  succession.  Be- 
ginning with  the  simplest  process  of  observation,  the  praxis 
is  carried,  by  successive  stages,  up  to  the  highest  and  most 
complex  processes  of  constructive  thinking,  and  the  mind 
capable  of  such  work  trained  intelligently  and  systematically 
to  clear,  distinct,  connected,  continuous,  and  constructive 
thought. 

To  the  various  writers  on  the  subject  of  Logic,  the  author 
would  acknowledge  his  indebtedness,  and  especially  to  Ueber- 
weg,  Hamilton,  Thomson,  Whately,  Mill,  Jevons,  Atwater, 
McCosh,  Davis,  Bowen,  and  Day. 

To  teachers  he  would  suggest  that  Part  I.  may  be  used 
in  the  earlier  stages  of  training,  and  the  remaining  parts 
reserved  for  a  later  stage.  In  the  use  of  the  text-book 
the  teacher  will  ordinarily  do  his  best  work  for  his  pupil  by 
drawing  largely  on  his  own  resources  for  material  for  praxis. 
Each  locality,  school-room,  branch  of  study,  and  experience 
will  suggest  innumerable  topics  of  fresh  and  living  interest, 
which  may  be  profitably  substituted  for  those  given  in  the 

text-book. 

D.  S.  GREGORY. 

LAKE  FOREST  UNIVERSITY,       1 
LAKE  FOREST,  ILL.,  August,  1881.  ) 


1 


INTRODUCTION. 

PAGE 

I.— NATURE  OF  LOGIC 9 

TOPIC  1. — OBJECT-MATTER  OP  LOGIC 10 

TOPIC  2. — PRACTICAL  AIM  OP  LOGIC  ....  13 
TOPIC  3. — PRINCIPLES  OR  LAWS  OF  THOUGHT  .  .  .17 

II.— DIVISIONS  OF  LOGIC 22 

PART    I. 

The  Logic  of  Conception  or  the  Term. 

CHAPTER    I. 
THE  FORMATION  OF  CONCEPTIONS  .        .    25 

SECTION  I.— OBSERVATION 26 

TOPIC  1. — THE  PREDICABLES  OR  THINGS  KNOWABLE  .  27 
TOPIC  2. — OBSERVATION  OF  THINGS  PREDICABLE  .  .  30 

SECTION  II. — CONCEPTION  PROPER 34 

TOPIC  1. — PROCESS  OP  CONCEPT-FORMING  .  .  .  .34 
TOPIC  2. — PRODUCT  OP  CONCEPT-FORMING.  .  .  .38 

SECTION  III.— CLASSIFICATION 41 

TOPIC  1. — PROCESS  OP  CLASSIFICATION  .  .  .  .41 
TOPIC  2. — EESULTS  OP  CLASSIFICATION  ....  44 

SECTION  IY. — DENOMINATION  OR  NAMING  .  .  .49 

TOPIC  1. — PROCESS  OF  NAMING 49 

TOPIC  2. — PRODUCTS  OF  NAMING 52 

1*  v 


VI  CONTENTS. 

CHAPTER     II. 

PACK 

THE   UNFOLDING  OF  CONCEPTIONS  .        .    56 

SECTION  I.— LOGICAL  PARTITION 57 

TOPIC  1. — FORMS  OP  LOGICAL  PARTITION  .        .        .        .59 
TOPIC  2— RULES  OP  LOGICAL  PARTITION  .        .        .        .60 

SECTION  II. — LOGICAL  DIVISION 64 

TOPIC  1. — FORMS  OF  LOGICAL  DIVISION     .       .       .       .65 
TOPIC  2.— RULES  OP  LOGICAL  DIVISION     .        .        .        .68 

SECTION  III.— LOGICAL  DEFINITION 75 

TOPIC  1.— KINDS  OP  DEFINITION 75 

TOPIC  2.— RULES  OF  LOGICAL  DEFINITION  ,    81 


PART     II. 

The  Logic  of  Judgment  or  the  Proposition. 

CHAPTER    I. 

THE  FORMATION  OF  JUDGMENTS  OR  PROP- 
OSITIONS       93 

SECTION  I.— PROCESS  or  JUDGMENT-FORMING  .  .  93 
TOPIC  1. — THE  ELEMENTS  OP  JUDGMENT  .  .  .  .93 
TOPIC  2. — VERIFICATION  OR  PROOF  OF  JUDGMENTS  .  .  98 

SECTION  II. — PRODUCTS  OF  JUDGMENT  ....  no 

TOPIC  1. — QUALITY  OF  JUDGMENTS Ill 

TOPIC  2. — QUANTITY  OF  JUDGMENTS 112 

TOPIC  3. — RELATION  OF  JUDGMENTS 116 

TOPIC  4. — GRAMMATICAL  COMBINATION  OF  JUDGMENTS  .  118 

CHAPTER    II. 

THE   UNFOLDING  OF  JUDGMENTS.   .        .  121 

SECTION    I.— DEVELOPMENT    OF    CONTAINED    JUDG- 
MENTS     121 

SECTION  II. — DEVELOPMENT  OF  IMPLIED  JUDGMENTS  123 
TOPIC  1. — SIMPLER  FORMS  OP  IMPLICATION  .  .  .  123 
TOPIC  2. — OBVERSION  .  .  123 


CONTENTS.  vii 

PAGE 

SECTION   III. — DEVELOPMENT    OF   INFERRED   JUDG- 
MENTS  125 

TOPIC  1. — INFERRED  JUDGMENTS  BY  ADDITIONS  .  .  126 
TOPIC  2. — INFERRED  JUDGMENTS  BY  DISJUNCTION  .  .  126 
TOPIC  3. — INFERRED  JUDGMENTS  BY  CONVERSION  .  .  126 
TOPIC  4. — INFERRED  JUDGMENTS  BY  OPPOSITION  .  128 


PART     III. 

The  Logic  of  Reasoning  or  the  Syllogism. 

CHAPTER    I. 

THE   FORMATION   OF  REASONING    OR   MEDI- 
ATE INFERENCES    .        .        .        .135 

SECTION  I. — PROCESS  OF  REASONING  IN  GENERAL     .  135 

TOPIC  1. — FORMS  OF  REASONING 135 

TOPIC  2. — ELEMENTS  OF  REASONING 137 

TOPIC  3. — FINDING  AND  VERIFYING  ARGUMENTS       .        .  139 

SECTION  II.— DEDUCTIVE  REASONING     .       .       .       .139 
TOPIC  1. — PROCESS  OF  VERIFYING  THE  ARGUMENT  IN  DE- 
DUCTION     139 

TOPIC  2. — PRODUCTS  OF  DEDUCTIVE  REASONING        .        .  141 

SECTION  III.— INDUCTIVE  REASONING  ....  147 
TOPIC  1. — VERIFYING  CAUSE  IN  INDUCTION  .  .  .  147 
TOPIC  2. — PRODUCTS  OF  INDUCTIVE  REASONING  .  .  157 

CHAPTER    II. 

THE   UNFOLDING   OF  REASONING   OR   THE 

SYLLOGISM 162 

SECTION  I. — THE  CATEGORICAL  SYLLOGISM  UNFOLDED  162 
TOPIC  1.— POSSIBLE  FORMS  OR  FIGURE  AND  MOOD  .  .  162 

TOPIC  2. — TESTING  OF  VALID  FORMS 164 

TOPIC  3.— COMPLEX  AND  ABNORMAL  FORMS      .        .        .  179 
SECTION    II.— THE   HYPOTHETICAL   SYLLOGISM   UN- 
FOLDED  185 

TOPIC  1. — CONDITIONAL  OR  CONJUNCTIVE  SYLLOGISM        .  185 


Vlll  CONTENTS. 

PAGE 

TOPIC  2. — DISJUNCTIVE  SYLLOGISM 188 

TOPIC  3. — DlLEMMATIC  SYLLOGISM 189 

SECTION  III.— CONSPECTUS  OF  FALLACIES     .       .       .191 

TOPIC  1. — FALLACIES  IN  INDUCTION 191 

TOPIC  2.— FALLACIES  IN  DEDUCTION  .  .  192 


PART    IV. 

The  Logic  of  Construction  or  the  System. 

CHAPTER    I. 

THE  FORMATION  OF  CONSTRUCTION  OR 

SYSTEM       .....  200 

SECTION  I.— SCIENTIFIC  CONSTRUCTION  .       .       .       .200 
TOPIC  1. — PROCESS  OF  FORMING  AND  VERIFYING  SCIEN- 
TIFIC SYSTEM 200 

TOPIC  2. — PRODUCTS  OF  SCIENTIFIC  CONSTRUCTION    .        .  202 
SECTION  II.— PRACTICAL  CONSTRUCTION       .       .       .206 
TOPIC  1. — PROCESS  OF  FORMING  AND  VERIFYING  PRAC- 
TICAL SYSTEM 206 

TOPIC  2. — PRODUCTS  OF  PRACTICAL  CONSTRUCTION    .        .  207 

CHAPTER    II. 
THE  UNFOLDING  AND  TESTING  OF  SYSTEMS.  207 

SECTION  I.— ASCERTAINING  THE  ELEMENTS.  .  .  208 
TOPIC  1. — THE  WHOLE  AND  ITS  PRINCIPLE  .  .  .  208 
TOPIC  2. — THE  ARTICULATION  OR  KELATION  OF  THE  PARTS  209 
TOPIC  3. — THE  RELATION  TO  THE  OBJECTIVE  REALITY  .  209 

SECTION  II.— TESTING  OF  SYSTEMS 210 

TOPIC  1. — DIRECTIONS  FOR  TESTING 210 

TOPIC  2.— EXAMPLES  ILLUSTRATIVE  ,  .211 


INDEX 213 


PRACTICAL  LOGIC, 

INTRODUCTION. 


I.   THE    NATURE    OF    LOGIC. 

What  is  Logic?  —  This  question  has  been  variously 
answered.  Whately  says  it  may  be  considered  as  "  the 
Science  and  also  as  the  Art  of  Reasoning."  Hamilton  de- 
fines it  as  "  the  Science  of  the  formal  and  necessary  Laws 
of  Thought  as  Thought."  Dr.  Watts  called  his  work,  "  The 
Art  of  Thinking."  According  to  his  view,  "  Logic  is  the 
art  of  directing  the  reason  aright  in  acquiring  the  knowl- 
edge of  things,  for  the  instruction  both  of  ourselves  and 
others." 

Without  stopping  to  discuss  these  definitions,  which  would  be  un- 
intelligible to  the  ordinary  student  at  the  outset,  it  is  clear  that  these 
different  authors  must  either  be  defining  different  things,  or  defining 
the  same  thing  from  different  points  of  view,  or  defining  different 
things  from  different  points  of  view.  "Reasoning"  and  "thought" 
are  different  things,  the  former  being  only  one  form  of  the  latter. 
The  points  of  view  of  science  and  art  are  different,  the  one  being 
theoretical,  the  other  practical. 

Definition. —  As  treated  in  the  present  work,  Logic  is  the 

Q 


10  PRACTICAL    LOGIC. 

Practical  Science  of  the  Principles  or  Laws  which  govern 
the  various  forms  of  correct  Thinking  or  Thought. 

This  definition  will  be  best  explained  by  considering  the 
following  Topics : 

Topic  I —The  Object-Matter  of  Logic, 
Topic  II— The  Practical  Aim  of  Logic, 
Topic  III— The  Principles  or  Laws  of  Thinking  or  Thought, 

Topic  First. —  The  Object-Matter  of  Logic  is  found  in 
the  Forms  of  Thinking  or  Thought. 

1.  What  is  Thinking  or  Thought  ? 

(1.)  In  a  loose  sense,  any  operation  of  the  human  soul  is 
sometimes  spoken  of  as  thought.  The  man  knows,  feels  and 
purposes  or  wills;  any  act  of  knowing,  feeling,  or  willing 
may,  in  this  loose  sense,  be  called  thinking.  The  term  is 
evidently  not  used  in  this  loose  sense  in  the  definition  of 
Logic. 

(2.)  In  a  stricter  sense,  thinking  or  thought  is  confined 
to  the  operations  of  the  intellect  or  power  of  knowing. 
In  popular  phrase,  it  is  any  act  of  the  head  as  distinguished 
from  the  heart  and  will  of  the  man.  In  this  sense,  "think- 
ing "  is  synonymous  with  "  knowing." 

The  main  office  of  the  human  intellect  is  to  know,  i.  e.,  first,  to 
apprehend  objects  in  themselves  and  their  phenomena  or  attributes ; 
and  secondly,  to  apprehend  objects  or  their  phenomena  in  their  con- 
nections or  relations.  The  first  of  these  forms  may  be  termed  simple 
apprehension,  or  intuition,  or  simple  knowledge ;  the  second,  thought- 
knowledge,  or  thought.  Logic  has  to  do  with  thought-knowledge,  or 
thought. 

To  state  the  same  thing  in  another  and  fuller  form,  the  cognitive 
power  or  intellect  of  man  performs  its  entire  office  of  knowing  in 
four  different  ways  ;  in  other  words,  it  has  four  different  faculties  : 

1st.  The  intellect  acquires  the  fundamental  facts  of  knowledge  of 
things  material  and  spiritual  by  the  senses  and  consciousness ;  and 
has,  therefore,  a  simple  cognitive  faculty.  Its  office  is  to  gather  the 
material  for  the  use  of  the  higher  faculties  of  thought. 


THE   NATURE    OF  LOGIC.  11 

2d.  The  intellect  keeps  the  acquired  knowledge  in  such  shape  as  to 
be  able  to  reproduce  it  for  use  at  any  time  when  it  may  be  needed  by 
the  higher  faculties  ;  and  has,  therefore,  a  conservative  faculty  or 
memory. 

These  two  faculties  furnish  knowledge  and  keep  it  at  command  for  use, 
and  their  operations  are  often  spoken  of,  in  a  loose  sense,  as  thought ; 
but,  using  thought  in  the  strict  sense,  it  is  often  truly  said  of  one  who 
uses  these  two  powers  with  great  ease,  "  He  never  had  a  thought  in 
his  life.  He  is  a  mere  man  of  memory.'' 

3d.  The  intellect  compares  the  knowledges  acquired  and  conserved, 
and  connects  them  into  conceptions,  judgments,  and  arguments  ;  and 
has,  therefore,  a  comparative,  or  elaborative,  faculty. 

4th.  The  intellect  groups  in  systems,  according  to  the  law  of  the 
true,  the  beautiful,  or  the  good,  the  knowledges  acquired  by  the  simple 
cognitive  faculty,  kept  and  reproduced  by  the  conservative  faculty, 
and  connected  in  thought  by  the  comparative  faculty  ;  and  has,  there- 
fore, a  system-making,  or  constructive,  faculty.  This  is  also  discursive. 

The  term  "  thinking"  or  "  thought "  is  often  applied  to  all  four  forms 
of  intellectual  action.  This  is  evidently  not  the  sense  in  which  it  is 
used  in  the  definition  of  Logic. 

(3.)  Thought  or  thinking,  strictly  speaking,  is  the  opera- 
tion or  product  of  the  operation  of  the  third  and  fourth  fac- 
ulties only,  i.  e.,  of  the  comparative  and  constructive  facul- 
ties only.  These  faculties  are  the  thought  faculties  ;  their 
operation  is  thinking ;  and  the  product  of  their  operation  is 
thought.  Ordinarily,  the  word  thought  is  used  for  any  or 
all  three  :  the  faculty,  its  exercise,  its  product.  These  fac- 
ulties are  also  called  discursive,  since  they  proceed  from 
simple  knowledges  to  new  results  founded  upon  them. 

2.  What  are  the  Forms  of  Thinking  or  Thought  ? 

The  forms  of  thinking  or  thought  are  the  forms  in  which 
the  discursive  or  thought  faculties  act,  or  the  products  of 
that  action. 

(1.)  As  thinking  is  embodied  in  language,  the  most  common  forms 
of  thought  may  be  learned  by  an  examination  of  thought  expressed 
in  language.  Take  the  following  example  :  Light  is  opposed  to  dark- 
ness ;  feathers  are  light ;  therefore,  feathers  are  opposed  to  darkness. 


12  PRACTICAL    LOGIC. 

This  is  in  the  form  of  a  syllogism.  A  syllogism  embodies  an  argu- 
ment, or  process  of  reasoning.  In  it  two  propositions  are  compared 
and  a  conclusion  reached  which  is  expressed  in  a  third  proposition. 
This  is  thought  as  reasoning. 

These  three  propositions  are  verbal  expressions  of  judgments,  in 
which  the  mind  compares  and  connects  two  terms.  This  is  thought 
as  judgment. 

Each  of  the  terms  in  these  propositions  is  a  thought,  and  must  be 
understood,  as  is  shown  by  the  example  given,  if  any  correct  think- 
ing is  to  be  done.  This  is  thought  as  conception. 

When  a  series  of  terms,  propositions,  arguments,  etc.,  is  grouped 
together  to  make  a  larger  whole  of  thought,  the  result  is  thought  as 
system. 

(2.)  Or  looking  at  the  subject  from  the  thought  side,  instead  of 
from  the  language  side,  the  same  result  is  reached. 

The  comparative  faculty  acts  in  three  ways :  a.  By  comparing  the 
objects  or  knowledges,  given  by  the  simple  cognitive  faculty  and  re- 
tained by  the  conservative  faculty,  and  connecting  them  by  resembling 
attributes  or  marks,  thus  forming  notions  or  concepts,  classes  and 
general  terms.  This  is  thought  as  conception,  b.  By  comparing 
concepts  or  general  terms  and  connecting  them  by  agreement  or  dis- 
agreement, resulting  in  judgments  and  propositions.  This  is  thought 
as  judgment,  c.  By  comparing  judgments  or  propositions  and  connect- 
ing them  by  the  principle  of  reason  and  consequent,  resulting  in  argu- 
ments including  syllogisms.  This  is  thought  as  reasoning. 

The  constructive  faculty  also  acts  in  three  ways :  a.  Grouping  by 
the  Law  of  the  True,  or  in  the  form  of  scientific  construction,  result- 
ing in  scientific  systems,  b.  Grouping  by  the  Law  of  the  Beautiful, 
or  in  the  form  of  artistic  or  aesthetic  construction,  resulting  in  artistic, 
or  aesthetic,  systems,  including  all  art  productions,  c.  Grouping  by 
the  Law  of  the  Good,  or  in  the  form  of  practical  construction,  result- 
ing in  practical  systems,  including  inventions,  plans  of  conduct,  etc. 

It  will  at  once  be  seen  that  the  second  of  these  forms  of  construc- 
tion falls  within  the  sphere  of  ^Esthetics,  leaving  only  the  first  and 
third  in  the  sphere  of  Logic. 

The  distinct  Forms  of  Thought  with  which  Logic  deals 
are,  therefore,  as  follows : 

Conception,  embodied  in  the  general  term ; 
Judgment,  embodied  in  the  proposition ; 


THE    NATURE    OF   LOGIC. 


13 


Reasoning1,  embodied  in  the  argument ; 
Construction,  embodied  in  system,  scientific  and  prac- 
tical. 

The  facts  concerning  the  workings  of  the  Human  Soul  may  be  tabu- 
lated so  as  to  present  their  relations  to  the  eye. 


THE  HUMAN  SOUL, 
or  Man,  the  Conscious 
Subject, 


Man,  by  the  COGNI- 
TIVE POWER, 


KNOWS,  and,  therefore,  has  a  Cog- 
nitive Power,  or  Intellect ; 

FEELS,  and,  therefore,  has  an  Emo- 
tive Power,  or  Sensibility ; 

WILLS,  and,  therefore,  has  a  power 
of  Endeavor,  or  Conative  Pow- 
er, or  Will. 


ACQUIRES  knowledges  by  the  Simple 
Cognitive  Faculty ; 

KEEPS  knowledges  by  the  Conserv- 
ative Faculty,  or  Memory ; 

COMPARES  knowledges,  or  works  out 
their  Relations  by  the  Comparative 
Faculty ; 

CONSTRUCTS  knowledges  into  Systems 
by  the  Constructive  Faculty. 


s  ~ 

9    ^ 
'    •* 


I 

1  5- 


COMPARES,    by 
the  Compara- 

tive Faculty, 

MAN,  by  the 
DISCURSIVE  • 

Faculties, 

CONSTRUCTS,  by 
the  Construct- 

ive Faculty, 

Simple  knowledges,  in  Con- 
ception ; 

Conceptions,  in  Judgment ; 
Judgments,  in  Reasoning. 

The  True,  in  Scientific  Sys- 
tem; 

The  Beautiful,  in  .Esthetic 
System  ; 

The  Good,  in  Practical  Sys- 
tem. 


Topic  Second. — The  Practical  Aim  of  Logic  is  to  train  to 
Correct  Thinking  or  Thought. 

Logic,  as  here  treated,  is  a  practical  science,  aiming  to 
lead  the  thinker  to  a  systematic  knowledge  of  the  laws  of 
2 


1  PRACTICAL    LOGIC. 

thought,  in  order  to  find  in  these  the  rules  by  which  to 
train  to  skill  in  right  thinking-. 

1.  What  is  Practical  Science  or  Art? 

A  science  is  a  complete  and  systematic  presentation  of  the  facts  and 
principles  in  any  sphere  of  knowledge,  in  accordance  with  truth. 
Hamilton  draws  from  Aristotle  the  distinction  between  Philosophy 
"  Theoretical  "  and  "  Practical."  "  Theoretical,  called  likewise  specu- 
lative and  contemplative,  philosophy  has  for  its  highest  end  mere 
truth  or  knowledge.  Practical  philosophy,  on  the  other  hand,  has 
truth  or  knowledge  only  as  its  proximate  end, — this  end  being  subor- 
dinate to  the  ulterior  end  of  some  practical  action."  Notwithstanding 
Hamilton's  objections  to  the  expressions,  they  are  in  common  use,  and 
will  doubtless  continue  in  use.  "Science"  and  "Art"  are  also  often 
used  to  express  substantially  the  same  distinction. 

The  sciences  and  arts  are  both  systematic  forms  of  human  knowl- 
edge. The  aim  of  a  science  is  to  give  systematic  knowledge  of  some- 
thing ;  that  of  an  art,  to  give  skill  in  doing  something.  The  one  calls 
for  the  study  of  scientific  principles  ;  the  other  for  the  intelligent  appli- 
cation to  practice  of  rules  based  upon  these  principles.  A  science  pre- 
sents truths  to  be  grasped  ;  an  art,  exercises  to  be  performed. 

Practical  Science,  or  Art,  as  it  is  sometimes  called,  is  a 
form  of  science  in  which  the  systematic  knowledge  of  the 
subject  treated  is  subordinate  to  the  training  to  skill  in 
some  activity. 

2.  How  far  is  Logic  Theoretical  and  how  far  Practical  ? 

Logic  is  a  theoretical  science,  or  science  proper,  so  far 
as  it  aims  to  give  a  systematic  view  of  the  laws  of  thought ; 
it  is  a  practical  science,  or  art,  so  far  as  it  subordinates 
this  to  its  aim  to  train  to  skill  in  applying  the  laws  of 
thought  in  avoiding  error  and  arriving  at  truth.  From  the 
scientific  side,  Logic  should  present  in  systematic  shape  the 
laws  which  govern  the  various  forms  of  thought,  or  the  laws 
by  which  the  mind  must  be  governed  when  it  thinks  cor- 
rectly, i.  e.,  when  it  conceives,  judges,  reasons,  systematizes 
correctly.  From  the  practical  side,  Logic  should  turn  these 


THE   NATURE    OF   LOGIC.  15 

laws  into  rules  and  train  the  mind  to  think  correctly  and 
efficiently,  by  training  it  to  use  these  rules  of  thought  intel- 
ligently and  skilfully.  It  should,  if  it  is  to  be  of  the  most 
service,  train  the  thinker  at  once  to  accuracy  of  thought  in 
reaching  truth  and  avoiding  error,  and  to  power  in  using 
the  thought-faculties, —  in  other  words,  it  should  train  both 
to  skill  and  power.  In  accordance  with  this  view,  Pro- 
fessor Bain  remarks,  that  although  "  Logic,  no  doubt,  has  a 
certain  theoretic  aspect,  ...  its  chief  aim  must  ever  be 
practical.  Had  the  subject  not  been  wanted  as  an  aid  to 
the  search  of  truth,  it  would  never  have  been  called  into 
existence." 

3.  Logic  aims  at  Correct  Thinking,  or  at  Truth. 

Logic  is  defined,  in  the  "  Port  Eoyal  Logic,"  as  "  the 
science  of  the  operations  of  the  understanding  in  the  pur- 
suit of  truth."  Logic  aims  at  correct  thinking.  Such 
thinking  is,  from  one  point  of  view,  thinking  that  is  done 
in  accordance  with  the  laws  of  thought  which  are  treated 
in  works  on  Logic.  From  another  point  of  view  it  is  think- 
ing which,  by  conformity  to  the  laws  of  thought,  arrives  at 
truth. 

(1.)  Truth. — In  order  to  understand  the  meaning  of  these  statements 
concerning  truth,  there  is  need  of  considering :  the  nature  and  crite- 
rion of  truth ;  the  modes  of  arriving  at  truth ;  the  degrees  of  assur- 
ance in  the  grasp  of  truth. 

a.  The  Nature  and  Criterion  of  Truth. 

According  to  Hamilton,  truth  is  "  the  correspondence  or  agreement 
of  a  cognition  with  its  object."  Or,  including  both  thought  and  state- 
ment, truth  is  the  agreement  of  a  thought  or  statement  with  the  reality 
which  the  thought  or  statement  concerns.  Error  is  the  opposite,  or 
the  want  of  harmony  between  a  thought  or  statement  and  its  object. 

The  criterion,  or  test  of  truth,  arises  out  of  its  nature  as  thus  stated. 
Does  it  correspond  with  the  reality  ?  "  Man  is  mortal."  "  The  sun 
shines."  "  Madagascar  is  inhabited."  "  The  earth  is  spherical."  In 
deciding  whether  these  statements  are  true,  the  question  to  be  asked 
of  each  is,  Does  it  agree  with  fact  or  reality  f 


16  PRACTICAL    LOGIC. 

b.  Modes  of  Arriving  at  Truth. 

The  truth  in  any  given  case  is  arrived  at  in  one  or  other  of  two 
ways : 

First,  by  the  use  of  one's  own  powers  intuitive  or  discursive.  These 
give  knowledge  in  the  narrower  sense.  The  intuitive  powers  furnish 
immediate  knowledge,  or  a  priori  knowledge :  (a.)  By  external  or  sense 
perception,  of  matter  and  its  phenomena ;  (6.)  By  internal  perception 
or  self-consciousness,  of  spirit  and  its  operations ;  (c.)  By  intuition 
proper,  of  the  self-evident  and  necessary  notions  and  principles  which 
underlie  and  condition  all  human  experience.  The  discursive  powers 
furnish  mediate  or  a  posteriori  knowledge  by  the  processes  of  thought, 
conception,  judgment,  reasoning,  and  construction. 

Secondly,  by  acceptance  of  the  statements  of  others.  These  give 
belief  in  the  narrow  and  strict  sense,  or  the  acceptance  of  truth  on  the 
ground  of  testimony.  Most  of  man's  knowledge  in  the  wide  sense, 
and  that  the  most  valuable  part  of  it,  is  derived  from  this  source. 
The  witnesses  gain  their  knowledge  either :  (a.)  By  the  use  of  their 
intuitive  powers,  which  lays  the  foundation  for  testimony  proper;  or, 
(6.)  By  the  use  of  their  discursive  or  thought  powers,  which  lays  the 
foundation  for  authority. 

o.  Degrees  in  the  Assurance  of  Truth. 

The  mind  does  not  lay  hold  of  all  its  knowledge  with  the  same  de- 
gree of  certainty.  Distinction  is  made  between  belief,  opinion,  proba- 
ble truth,  certain  truth. 

Certainty  is  the  consciousness  of  the  necessity  of  agreement  between 
a  thought  and  its  object,  in  whichever  of  the  above  ways  that  thought 
may  be  reached.  It  absolutely  excludes  the  admission  of  any  opposite 
supposition.  Where  this  is  not  the  case,  doubt  and  uncertainty  arise. 

Considered  with  reference  to  the  degree  of  certainty,  there  appear, 
at  the  two  extremes : 

Knowledge,  in  the  strictest  sense,  where  the  consciousness  of  neces- 
sity is  absolute,  or  certainty  perfect ; 

Opinion,  or  the  admission  of  something  where  the  evidence  is  not 
such  as  to  necessitate  a  perfect  certainty. 

Probability  appears  in  the  approximation  of  the  imperfect  certainty 
of  opinion  to  the  perfect  certainty  of  knowledge. 

Belief  is  used  in  various  loose  senses,  but  the  distinction  given  above 
will,  it  is  thought,  commend  itself  as  the  fundamental  sense.  Belief 
is  the  acceptance  of  truth  on  the  ground  of  testimony,  including  testi- 
mony proper  and  authority. 


THE    NATURE    OF  LOGIC.  17 

(2.)  Truth  by  Thought. — The  aim  of  Logic  is  to  arrive  at  truth 
through  the  powers  of  thinking  or  thought.  The  grasp  of  the  truth 
reached  will  evidently  depend  upon  the  kind  of  truth  and  the  accu- 
racy of  the  thinking.  Correct  thinking  will  give  a  more  or  less  cer- 
tain grasp  of  the  truth  reached  as  the  result  of  it.  In  mathematical 
and  intuitive  truth  the  result  reached  is  absolutely  certain.  In  other 
regions  of  thought  the  results  of  thought  are  more  or  less  probable. 
These  varying  degrees  of  certainty  may  be  illustrated  by  examples. 
It  is  certain  that  two  and  two  cannot  but  make  four  ;  that  things 
which  are  equal  to  the  same  thing  are  equal  to  each  other  ;  that  every 
event  must  have  a  cause.  It  is  probable  that  the  first  day  of  January, 
1900,  will  be  cold.  It  is  extremely  probable  that  the  sun  will  rise 
to-morrow.  It  is  probable  that  a  young  man  of  good  capacity,  char- 
acter, and  habits  will  succeed  in  business.  It  is  the  opinion  of  certain 
astronomers  that  the  moon  is  uninhabited.  It  is  the  belief  of  most 
intelligent  men  that  the  earth  is  about  93,000,000  miles  from  the  sun. 

Topic  Third.— The  Principles  or  Laws  of  Thinking  or 
Thought. 

Logic  deals  with  the  principles  or  laws  which  govern 
thought. 

Every  rational  human  activity  proceeds  according  to  definite  laws, 
known  or  unknown.  The  highest  degree  of  intelligence  and  efficiency 
in  any  such  activity  requires  that  the  laws  be  known  and  correctly 
made  use  of  in  directing  the  activity.  This  is  true  of  the  various 
forms  of  thought ;  they  have  their  laws  which  govern  their  action. 
There  are  laws  of  conception,  laws  of  judgment,  laws  of  reasoning, 
laws  of  construction.  Logic  should  enable  the  thinker  to  ascertain 
and  apply  these  laws,  and  thus  aid  him  in  correct  thinking  and  save 
him  from  incorrect  thinking.  It  is  likewise  true  that  the  highest 
degree  of  intelligence  and  efficiency  in  thinking  requires  a  thorough 
knowledge  of  the  laws  of  thought  and  a  correct  use  of  them  in  guid- 
ing the  exercise  of  thought.  Practical  Logic  should  aim  to  give  the 
thinker  the  most  thorough  knowledge  of  the  laws  and  the  greatest 
efficiency  in  using  them  in  thinking. 

Besides  the  special  laws  which  govern  the  various  forms 

of  thought,  there  are  certain  general  laws,  certain  axioms 

or  fundamental   laws   and  certain   postulates  with  which 

Logic  sets  out.     The  special  laws  will  be  unfolded  in  con- 

2*  B 


18  PRACTICAL    LOGIC. 

nection  with  the  treatment  of  the  various  forms  of  thought ; 
at  the  outset  must  be  presented  the  fundamental  laws  and 
postulates. 

1,  The  Fundamental  Laws  of  Thought. 

Logic,  like  other  sciences,  has  certain  fundamental  prin- 
ciples upon  which  the  more  special  laws  rest.  These  are 
usually  reduced  to  four : 

The  Law  of  Identity,  or  Affirmation ; 

The  Law  of  Contradiction,  or  Negation  ; 

The  Law  of  Excluded  Middle,  or  Exclusion  ; 

The  Law  of  Reason  and  Consequent,  or  Sufficient  Reason. 

(1.)  The  Law  of  Identity,  or  Affirmation. 

The  Law  of  Identity  may  be  stated  as  follows :  Every- 
thing is  identical  with  itself,  or  is  what  it  is,  and  we  may 
affirm  this  of  it.  This  has  been  formulated  :  A  is  A ;  or 
A  =  A.  Whatever  is,  is. 

The  identity  may  be :  a.  Absolute,  or  that  of  total  sameness  of  a 
thing  or  thought  with  all  its  parts ;  or,  6.  Relative,  or  that  of  partial 
sameness  of  a  thing  or  thought  with  each  or  some  of  its  parts.  The 
logical  concept  or  notion  expressed  by  the  general  term,  man,  is  made 
up  of  the  following  elements :  being,  material,  organized,  animated, 
rational,  terrestrial.  Man  is,  therefore,  totally  identical  with  all  these 
elements ;  so  that  it  may  be  correctly  affirmed  that  man  is  material, 
organized,  animated,  rational,  terrestrial  being.  Man  is  partially  iden- 
tical with  any  of  these  elements ;  so  that  it  may  be  correctly  affirmed 
that  man  is  material ;  man  is  organized,  etc. 

The  Law  of  Identity  gives  the  logical  right  to  affirm  such 
total  or  partial  identity  in  all  cases  where  it  exists.  It  is 
at  the  basis  of  all  consistent  affirmative  thinking, —  of  all 
positive  conceptions,  logical  definitions,  affirmative  judg- 
ments, and  categorical  arguments. 

(2.)  The  Law  of  Contradiction,  Negation,  or,  as  Ham- 
ilton terms  it,  Non-contradiction,  may  be  stated  as  fol- 


THE   NATURE    OF  LOGIC.  19 

lows :  Everything  is  not  what  it  is  not,  and  we  may  affirm 
this  of  it.  Or,  conflicting  attributes  cannot  co-exist  in  and 
may  not  be  affirmed  of  the  same  object.  This  has  been 
formulated :  A  is  n't  not  -A.  Nothing  can  both  be  and 
not  be. 

The  logical  concepts  expressed  in  the  following  pairs  of  general 
terms  are  contradictories :  black  and  not-black ;  round  and  not-round ; 
good  and  wicked ;  finite  and  infinite.  We  are  logically  excluded  from 
affirming  the  co-existence  of  these  mutually  contradictory  thoughts  or 
things.  A  thing  cannot  be  black  and  not-black  at  the  same  time  and 
in  the  same  sense.  A  door  cannot  be  open  and  shut  (not-open)  at  the 
same  time  and  in  the  same  sense.  Black-white,  round-square,  good- 
wickedness,  finite-infinitude,  combine  mutual  contradictories,  and  are, 
therefore,  logically  excluded  from  correct  thought  by  this  law. 

The  law  of  non-contradiction  is  the  complement  of  that 
of  identity.  Its  importance  arises  from  the  fact  that  it 
is  at  the  basis  of  all  logical  negation  and  distinction  in 
thought, —  of  all  negative  conceptions  and  judgments. 

(3.)  The  Law  of  Excluded  Middle,  or  Exclusion,  may  be 

stated  as  follows  :  Of  two  contradictories  one  must  be  true 
and  the  other  false.  If  one  is  affirmed,  the  other  is  thereby 
denied.  One  excludes  the  other,  and  hence  there  can  be 
no  medium  affirmation  between  the  two.  This  axiom  has 
been  formulated  :  A  either  is  or  is  not.  A  either  is  or  is 
not  B.  Everything  must  either  be  or  not  be. 

E.  g.,  An  intra-mercurial  planet,  Vulcan,  exists  or  does  not.  The 
moon  either  is  inhabited  or  it  is  not.  Bacon  either  was  Shakespeare 
or  he  was  not.  The  two  propositions,  Vulcan  exists,  Vulcan  does  not 
exist,  are  first  tested  by  the  Laws  of  Identity  and  Contradiction.  If 
by  the  Law  of  Identity  it  is  true  that  Vulcan  exists,  then,  by  the 
Law  of  Exclusion,  the  proposition,  Vulcan  does  not  exist,  must  be 
false.  If  by  the  Law  of  Contradiction  it  be  true  that  Vulcan  does 
not  exist,  then,  by  the  Law  of  Exclusion,  the  proposition,  Vulcan 
exists,  must  be  false. 

The  importance  of  the  Principle  of  Exclusion  arises  from 


20  PRACTICAL    LOGIC. 

its  being  the  foundation  of  all  disjunctive  judgments,  i. «., 
"  of  judgments  in  which  a  plurality  of  judgments  are  con- 
tained, and  which  stand  to  each  other  in  such  a  reciprocal 
relation  that  the  affirmation  of  one  is  the  denial  of  the 
other." 

(4.)  The  Law  of  Reason  and  Consequent,  or  Sufficient 
Reason. —  The  Law  is  stated  as  follows:  All  continuous 
thought  must  be  rationally  connected.  The  Law  has  been 
formulated  :  Infer  nothing  without  a  ground  or  reason.  The 
starting-point  in  continuous  thinking  is  the  affirmation  of 
some  knowledge  by  which  the  mind  is  necessitated  to  affirm 
or  posit  something  else.  This  starting-point  is  called  the 
logical  reason,  ground,  or  antecedent,  or,  as  Hamilton  sug- 
gests, condition;  that  something  else  which  the  mind  is 
necessitated  to  affirm  or  posit  is  called  the  logical  conse- 
quent, or  the  conditioned ;  the  relation  between  the  reason 
and  consequent  is  called  the  logical  connection  or  consequence. 

Reason  and  consequent  involve  not  only  cause  and  effect,  but  every 
case  where  an  antecedent  compels  the  mind  to  affirm  something  else, 
as  logically  following  it.  It  includes  the  relations  of  whole  to  part, 
cause  to  effect,  substance  to  attribute,  etc.,  with  the  reversed  relations 
of  part  to  whole,  effect  to  cause,  attribute  to  substance,  etc. 

The  axiom,  as  presented  by  Hamilton,  takes  a  positive  and  a  nega- 
tive form. 

(a.)  Positive  Form. — "When  a  reason  is  explicitly  or  implicitly 
given,  then  there  must  exist  a  consequent ;  and,  vice  versa,  when  a 
consequent  is  given,  there  must  also  exist  a  reason."  The  presence  of 
a  tree  as  a  whole  always  implies  the  presence  of  any  or  all  of  its  parts, 
—  roots,  trunk,  branches.  The  presence  of  any  attribute,  as  intelli- 
gence, always  implies  the  presence  of  the  substance  of  which  it  is  an 
attribute, —  mind. 

(b.)  Negative  Form. — Where  there  is  no  reason,  there  can  be  no 
consequent  (either  implicitly  or  explicitly).  Where  there  is  no  con- 
sequent, there  can  be  no  reason.  The  absence  of  mind  involves  the 
absence  of  memory  as  an  attribute  of  mind.  The  absence  of  will 
implies  the  absence  of  moral  accountability,  of  which  it  is  an  attribute. 


THE   NATURE    OF  LOGIC.  21 

The  logical  significance  and  value  of  the  Law  of  Keason 
and  Consequent  lies  in  this,  "  that,  in  virtue  of  it,  thought 
is  constituted  into  a  series  of  acts  all  indissolubly  con- 
nected; each  necessarily  inferring  the  other."  Without  it, 
continuous  and  connected  thought  or  reasoning  would  be 
impossible. 

2.  The  Postulates  of  Logic. 

There  are  certain  fundamental  postulates,  or  practical 
propositions,  assumed  at  the  outset  of  the  treatment  of 
Logic.  The  two  here  emphasized  respect  the  reality  of 
truth,  and  the  requirement  of  full,  explicit  statement. 

(1.)  The  First  Postulate, — There  is  such  a  thing  as  truth, 
which  can  be  ascertained,  and  on  which  all  minds,  acting 
in  accordance  with  the  laws  of  thought,  must  agree. 

Without  this  assumption  there  can  be  no  starting-point 
for  thought,  and  no  goal  for  the  activity  of  the  thought- 
power.  No  two  minds  could  otherwise  have  any  common 
basis  from  which  to  start  together  or  on  which  to  come  to- 
gether in  thinking  or  discussion. 

(2.)  The  Second  Postulate. — This,  as  stated  by  Hamilton, 
is,  "  to  be  allowed  to  state  explicitly  in  language  all  that  is 
implicitly  contained  in  thought."  Logic  deals  ultimately 
with  thought,  and  it  has  to  do  with  language  only  as  ex- 
pressing thought.  It  is,  therefore,  proper  to  ask,  in  connec- 
tion with  any  term,  proposition,  or  argument,  "  What  is  the 
thought  in  this?"  or,  in  other  words,  "What  is  the  full 
and  exact  meaning  of  this?"  and  to  state  in  full  this 
meaning.  Abridged  forms  are  to  be  completed,  rhetorical 
forms  to  be  translated  into  plain  language,  and  expressions 
changed,  if  need  be  (provided  the  thought  be  preserved), 
until  the  thought  is  brought  out  naked  and  entire.  Mill 
states  this  postulate  as  follows :  "  Logic  postulates  to  be 
allowed  to  assert  the  same  meaning  in  any  words  which  will 


22  PRACTICAL    LOO  1C. 

express  it ;  we  require  the  liberty  of  exchanging  a  propo- 
sition for  any  other  that  is  equipollent  (that  is,  having  equal 
power  and  reach)  with  it." 


II.   THE    DIVISIONS    OF    LOGIC. 

WHAT  are  the  Divisions  under  which  Logic  should  be 
presented  ?  This  question  has  been  variously  answered. 
The  answer  should,  in  any  case,  depend  upon  the  point  of 
view  and  object  of  the  work. 

The  most  common  division  is,  perhaps,  into  Pure  Logic 
and  Applied  Logic.  Hamilton  divides  it  into  Pure  and 
Modified.  Regarded  as  a  Practical  Science,  it  is,  perhaps, 
better  to  base  its  divisions  on  the  various  Forms  of  Thought. 

1.  Distinction  of  Pure  and  Applied  Logic. — The  logical 
writers  who  follow  the  common  division  find  it  necessary  to 
define  and  distinguish  Pure  and  Applied  Logic,  or  Theo- 
retical and  Practical  Logic.  As  these  terms  will  constantly 
be  met  with  in  the  works  on  Logic,  a  brief  explanation  of 
them  will  here  be  given. 

(1.)  Pure  Logic  is  the  Science  of  the  Necessary  and 
Formal  Laws  of  Thought  as  Thought.  It  treats  of  the 
necessary  laws  of  thought,  in  the  strict  sense  of  discursive 
thought,  as  they  are  in  themselves,  whatever  may  be  the 
object-matter  to  which  they  are  applied.  In  this  sense 
Logic  is  a  science  of  abstractions,  like  pure  mathematics  or 
metaphysics.  As  furnishing  the  principles  implied  in  and 
underlying  the  construction  of  all  other  Sciences,  it  has  also 
been  called  "  the  science  of  sciences." 

(2.)  Applied  Logic  treats  of  the  application  of  the  prin- 
ciples, or  laws  of  thought,  unfolded  in  Pure  Logic,  to  the 
investigation  of  truth.  It  assists  in  ascertaining  and  fol- 


THE    DIVISIONS    OF  LOGIC. 


23 


lowing  right  processes  of  thought  and  in  avoiding  wrong 
processes. 

This  division  is  the  same  as  the  distinction  of  the  School- 
men, of  Logica  Docens  and  Logica  Utens ;  of  the  Wolfian 
School  in  Germany  into  Theoretical  and  Practical ;  also,  as 
General  and  Special,  Abstract  and  Concrete. 

The  following  Outline  presents  the  common  Divisions  of 
Logic  from  this  point  of  view  : 


LOGIC,  the  Science 
of  the  Laws  of  Dis- 
cursive Thought, 
comprises  — 


I.  THEORETICAL,  or 
PUEE,  LOGIC,  or 
the  Science  of 
these  Laws 
themselves, 
eluding — 


m 
in- 


II.  PEACTICAL,  or 
APPLIED,  LOGIC, 
including  — 


1.  Laws  of  Conception. 

2.  Laws  of  Judgment. 

3.  Laws  of  Eeasoning. 

1.  The  Doctrine  of  Fal- 

lacies, or  the  modes 
of  avoiding  incor- 
rect thinking. 

2.  Method,  or  the  right 

modes  of  ascertain- 
ing truth. 


2.  Distinction  of  Pure  and  Modified  Logic, — Sir  William 
Hamilton  divides  Logic  into  Pure  and  Modified :  confining 
attention  to  Abstract  or  General  Logic. 

(1.)  Pure  Logic,  in  the  Hamiltonian  sense,  "  considers 
Thought  Proper  simply  and  in  itself,  and  apart  from  the 
various  circumstances  by  which  it  may  be  affected  in  its 
actual  application.  But  human  thought,  it  is  evident,  is 
not  exerted  except  by  men  and  individual  men."  It  is, 
therefore,  variously  modified  by  individual  peculiarities, 
original  and  acquired,  and  by  the  circumstances  of  the 
thinker.  Hence  arises  — 

(2.)  Modified  Logic,  which  considers  "the  conditions  to 
which  thought  is  subject,  arising  from  the  empirical  circum- 


24  PRACTICAL    LOGIC. 

stances,  external  and  internal,  under  which  exclusively  it 
is  the  will  of  our  Creator  that  man  should  manifest  his  fac- 
ulty of  thinking." 

For  Hamilton's  Divisions,  see  Hamilton's  "Logic,"  page 
49. 

3.  Divisions  based  on  the  Forms  of  Thought. — In  treat- 
ing Logic  as  a  Practical  Science,  it  is  more  convenient  and 
satisfactory,  if  not  more  logical,  to  base  the  divisions  on  the 
various  Forms  of  Thought, —  Conception,  Judgment,  Rea- 
soning, and  System.  It  is  more  convenient  and  satisfac- 
tory, since  by  this  method,  first,  the  learning  of  the  princi- 
ples will  go  hand  in  hand  with  their  use ;  secondly,  the 
scientific  view  will  be  kept  in  strict  subordination  to  the 
practical  end  aimed  at.  It  is  more  logical,  since  in  this 
way  it  is  believed  that,  first,  the  subjects  of  Fallacies  and 
of  Method  will  fall  into  their  natural  places,  in  connection 
with  the  presentation  of  the  laws  of  correct  thinking ; 
secondly,  the  whole  subject  will  take  such  shape  as  is  best 
to  train  to  skill  and  power  in  right  thinking  and  in  testing 
the  products  of  thought. 

According  to  this  view,  Logic  will  be  treated  under  four 
Divisions : 

PART  FIRST.     Logic  of  Conception,  or  of  the  Term. 
PART  SECOND.    Logic  of  Judgment,  or  of  the  Proposition. 
PART  THIRD.     Logic  of  Reasoning,  or  of  the  Syllogism. 
PART  FOURTH.  Logic  of  Construction,  or  of  the  System. 


PART  I. 

THE  LOGIC  OF  CONCEPTION  OR  THE  TERM. 

THE  aim  of  the  Logic  of  Conception  is  to  train  the  mind 
to  skill  in  dealing  with  the  first  and  fundamental  Form  of 
Thought. 

Definition. — Conception  is  that  form  of  thought  in  which 
we  compare  various  acquired  knowledges  and  connect  them 
by  resembling  marks  or  attributes,  thus  forming  Concepts, 
Classes,  and  General  Terms. 

This  definition  suggests,  as  a  first  subject  for  treatment, 
the  formation  of  conceptions.  The  every-day  practical 
necessity  for  studying  and  logically  testing  the  work  of 
thinkers,  as  embodied  in  their  scientific,  philosophic,  and 
literary  productions,  suggests,  as  a  second  subject,  the  un- 
folding1 of  conceptions.  The  Logic  of  Conception  will, 
therefore,  be  treated  in  two  Chapters. 

CHAPTER    I. 

THE  FORMATION  OP  CONCEPTIONS. 

WORKS  on  Logic  are  usually  mainly  confined  to  the  work 
of  unfolding  thought ;  but  as  the  process  of  forming  con- 
ceptions furnishes  the  key  to  their  unfolding,  it  will  be  first 
3  25 


26  PRACTICAL    LOGIC. 

considered.  The  definition  of  conception  suggests  the  four 
elements  of  the  process,  to  be  treated  in  as  many  Sections : 

First,  the  gathering  of  the  materials  for  conception,  i.e., 
the  knowledges  or  objects  of  thought.  This  is  the  work  of 
Observation. 

Second,  the  placing  of  these  materials  side  by  side, 
noting  the  resembling  parts,  marks,  or  attributes,  and 
gathering  these  into  thoughts,  called  concepts.  This  is 
Conception  proper. 

Third,  the  gathering  of  the  objects,  to  which  these  con- 
cepts or  bundles  of  common  attributes  apply,  into  classes. 
This  is  Classification. 

Fourth,  the  embodying  of  both  concepts  and  classes  in 
names,  or  general  terms.  This  is  Denomination. 

The  skilful  thinker  will  need  to  have  command  of  the  laws  of  these 
four  elements  of  Conception :  Observation,  Conception  proper,  Classi- 
fication, and  Denomination.  The  last  three  will  be  seen  in  their 
formation  to  involve  comparison  as  an  essential  element.  In  the 
treatment  of  the  three  in  the  First  Chapter,  both  the  process  and 
product  will  be  considered.  The  unfolding  of  the  products  of  the 
three  —  the  concept  proper,  the  class,  and  the  term  —  by  Partition, 
Division,  and  Definition,  will  be  the  work  of  the  Second  Chapter. 

Section  I.—  Observation. 

Strictly  speaking,  Observation  is  a  condition  rather  than 
an  element  of  conception.  It  must  always  precede  the 
proper  work  of  conception,  since,  without  careful  examina- 
tion of  the  objects  or  facts  about  which  the  work  of  think- 
ing is  done,  no  material  would  be  furnished  in  fit  shape  for 
the  use  of  thought  in  its  first  form. 

Definition. — Observation  is  the  mental  process  by  which 
we  gain  a  minute  and  comprehensive  knowledge  of  objects 
and  their  make-up. 

The  Instruments  of  Observation  are  the  Senses  and  Consciousness. 
In  gaining  a  knowledge  of  the  external  or  material  world,  the  ob« 


THE   FORMATION   OF   CONCEPTIONS.         27 

server  must  make  use  of  his  five  senses.  This  is  observation  in  the 
narrow  sense.  In  gaining  a  knowledge  of  the  facts  of  the  inner 
world,  or  world  of  mind,  he  must  make  use  of  consciousness,  or  inter- 
nal perception.  This  is  sometimes  known  as  reflection,  or  introspec- 
tion, and,  with  observation  by  the  senses,  makes  up  observation  in 
the  wide  sense. 

Topic  First.  The  Predicables,  or  Things  Knowable  or 
Nameable. — The  first  thing  in  order  to  observe  well  for  the 
purpose  of  correct  thinking  is  to  know  the  kinds  of  things 
that  may  be  known,  or  what  the  observer  may  expect  to 
find.  This  will  furnish  him  with  the  clew  needed  to  make 
his  observation  exact  and  complete  in  gathering  his  material 
for  thinking. 

From  another  point  of  view,  the  kinds  of  things  know- 
able  or  nameable  are  called  the  categories  (from  a  Greek 
word  meaning  to  predicate),  or  the  predicates  (from  the 
Latin,  meaning  to  assert),  or  the  predicables,  since  they 
sum  up  what  may  be  predicated  or  asserted  of  anything. 

It  should  manifestly  be  the  aim  of  every  intelligent  man  to  acquire 
the  power  to  know  as  much  as  possible  of  what  may  be  known  and 
named. 

1.  The  Predicables. — Starting  with  being,  or  thing,  as 

the  conception  including  all  things  in  the  universe,  a  simple 
classification  may  be  made  which  will  be  of  practical  value 
to  the  observer.  Being  always  appears  as  substance  having 
properties  or  attributes.  Properties  may  be  divided  into 
four  kinds,  reducible  to  three  : 

1st,  Properties  of  quality,  or  those  which  constitute  any- 
thing what  it  is. 

2d.  Properties  of  action,  or  those  which  manifest  the 
active  and  passive  powers  of  any  being. 

3d.  Properties  of  condition,  or  those  which  express  the 
connections  of  beings  with  space  and  time. 

4th.  Properties  of  relation,  or  those  which  express  the 
connections  of  beings  with  other  beings. 


28  PRACTICAL    LOGIC. 

The  properties  or  attributes  of  condition  and  relation 
are  sometimes  known  together  as  properties  of  relation  in  the 
wide  sense,  and  the  scheme  thus  reduced  to  three  kinds  of 
properties. 

Substance  and  property  and  the  kindred  terms  need  to 
be  carefully  distinguished. 

1.  Substance  is  used  in  two  kindred  meanings:  first,  as  being,  in 
contrast  to  and  independent  of  its  properties,  as  that  which  exists 
absolutely  and  of  itself,  absolute  being;   second,  "as  conjoined  with 
the  attributes  "  and  furnishing  their  basis,  that  which  stands  under 
and  supports  the  attributes,  the  thing  back  of  all  phenomena  "  which 
is  and  abides."     In  the  latter  and  more  common  meaning,  substance  is 
divided  into  matter  and  spirit,  or  that  which  is  extended  and  that 
which  thinks.     Subject  is  used  in  the  more  recent  philosophy,  es- 
pecially German,  to  denote  the  spirit,  "  the  basis  of  the  various  mental 
phenomena."     Conscious  subject  means  the  thinker  or  the  mind  itself. 
Object  is  a  term  for  that  about  which  the  knowing  subject  is  conver- 
sant.    Subjective  is  applied  to  that  which  belongs  to  or  proceeds  from 
the  conscious  subject;  objective,  to  that  which  belongs  to  01  proceeds 
from  the  object  known. 

2.  Various  properties — called,  also,  attributes,  qualities,  parts,  marks, 
characteristics,  phenomena,  etc. — are  the  materials  to  be  gathered,  in 
connection  with  substance,  for  conception.    These  terms  are  often  used 
in  a  loose  sense  as  synonymes.     The  first  three — property,  attribute, 
quality — are  the  most  important,  from  the  point  of  view  of  logic,  and 
need  to  be  carefully   distinguished ;    the  others  sufficiently  explain 
themselves.      Property  may  be  regarded  as  the  widest  of  the  three 
terms,  and  as  including  whatever  belongs  to  or  pertains  to  any  object 
of  knowledge.   Quality,  etymologically,  is  that  which  makes  anything 
what  it  is,  and  may,  therefore,  be  properly  regarded  as  including  the 
essential  properties,  called,  in  the  Scheme  given,  properties  of  quality. 
With  Aristotle  and  Descartes,  attributes  are  real  properties,  essential 
and  inherent.      They  may  be  restricted  to  properties  of  quality,  or 
extended  so  as  to  include  properties  of  action. 

Properties  may  be  distinguished  as  intrinsic  and  extrinsic.  The 
intrinsic  properties  of  any  object  of  knowledge  are  those  which  are 
inherent  in  the  object  itself.  In  the  Categories  the  properties  of  quality 
and  action  may  be  regarded  as  intrinsic.  Intrinsic  properties  may 
be  looked  upon  as  including  what  are  sometimes  called  peculiar  prop~ 


THE   FORMATION   OF    CONCEPTIONS.         29 

erties  and  inseparable  accidents.  The  extrinsic  properties  of  any 
object  are  those  which  arise  from  its  connection  with  something  exter- 
nal rather  than  from  its  own  nature.  They  include  the  properties  of 
condition  and  relation. 

Properties  are  also  distinguished  as  essential  and  non-essential.  An 
essential  property  is  one  of  those  which  make  any  object,  class,  or 
species  what  it  is,  as,  in  man,  the  faculties  of  sense  and  intelligence ; 
in  body,  the  dimensions  of  length,  breadth,  and  thickness.  An  essen- 
tial property  might  appropriately  be  called  a  quality,  in  the  strict 
etymological  sense.  The  essential  properties  of  any  object,  or  those 
which  make  it  what  it  is,  are  known  as  its  essence  or  (in  the  old  Logic) 
its  definition.  Non-essential  properties  are  those  which  do  not  belong 
to  the  essence  of  an  object.  Essential  properties  are  substantially  the 
same  as  intrinsic,  and  non-espential  as  extrinsic.  The  former  may  be 
looked  upon  as  embracing  properties  of  quality  and  of  action ;  the 
latter,  properties  of  condition  and  relation. 

Note.— Logicians  have,  from  the  earliest  times,  made  use  of  the  distinctions 
of  peculiar  property  (often  called  simply  property)  and  of  accidental  property, 
or  accident.  A  peculiar  property  has  been  defined  to  be  one  which  is  common 
to  the  whole  of  a  class  of  objects,  but  is  not  necessary  to  mark  off  that  class 
from  other  classes.  "  Capable  of  speaking  correctly  "  is  said  to  be  a  peculiar 
property  of  man,  not  embraced  in  the  definition  or  essence  of  man,  "  rational 
animal."  "  It  is,  however,"  as  Thomson  has  shown,  "  a  part  of  the  essence, 
for  rational  implies  it.  In  like  manner,  all  the  properties  seem  to  be  implicitly 
contained  in  every  perfect  definition.  No  criterion  can  be  given  for  distin- 
guishing between  the  essence  and  the  inseparable  accompaniment  of  the 
essence ;  and  a  larger  acquaintance  with  the  nature  of  things  makes  it  evident 
that,  what  one  science  regards  as  a  property,  another  must  consider  as  essen- 
tial, and  that  there  is  no  one  paramount  quality  which  is  absolutely  essential 
and  can  never  be  degraded  to  the  rank  of  a  property." 

An  accidental  property,  or  accident,  is  one  which  may  indifferently  belong 
or  not  belong  to  the  objects  of  any  class  without  affecting  their  essence.  The 
birthplace  of  a  man  and  the  clothes  he  wears  are  accidents  which  have  no 
necessary  effect  upon  his  manhood.  Accidents  are  separable  or  inseparable. 
A  separable  accident  is  one  that  can  be  changed,  as  the  clothes  of  a  man,  his 
position,  and  many  other  circumstances.  An  inseparable  accident  is  one  that 
can  never  be  changed,  although  it  may  have  no  necessary  connection  with 
essential  properties,  as  the  birthplace  of  a  man,  his  height,  etc.  Thomson  has, 
however,  shown  that  it  is  often  difficult,  if  not  impossible,  to  distinguish  acci- 
dent from  essential  property.  Writing  in  England,  he  says:  "  It  is  an  accident 
to  the  people  of  this  country  that  they  were  born  in  it ;  because  we  might  con- 
ceive them  to  have  been  born  elsewhere ;  but  then  it  has  modified  their  nature 
or  essence,  and  we  understand  by  Englishman  not  merely  one  who  was  born 
within  the  four  seas,  but  a  man  of  particular  feelings,  views,  and  privileges, 
which  are  parts  of  his  very  nature.  Here  accident  and  genus  or  property  seem 
to  become  confused." 
3* 


30  PRACTICAL   LOGIC, 

It  is,  therefore,  proposed  to  abandon  these  distinctions  as  at  least  unneces- 
sary for  logical  purposes. 

The  Scheme  of  Predicables,  therefore,  becomes : 
f  Substance, 


BEING,  j   Properties,  or 

Modes    of 
Substance, 


Quality,       I  Intringic  and  Essential 

Action,        J 

Condition,  ^ 


Relation, 


Extrinsic  and  Non-essential. 


The  old  Aristotelian  logicians  looked  upon  all  existing  things  as 
being  divided  by  nature  into  ten  classes  or  categories.  These,  accord- 
ing to  Aristotle,  are:  substance,  quantity,  quality,  relation,  place, 
time,  posture,  possession,  action,  passion.  A  thing  that  can  be  known 
or  named  comes  under  one  or  other  of  these  categories.  As  will  be 
seen  at  a  later  stage  in  the  study  of  Logic,  the  categories  will  not 
stand  the  test  of  the  laws  of  accurate  division. 

It  will  readily  be  seen  that  these  categories  of  Aristotle  may  all  be 
placed  under  one  or  other  of  the  categories  of  the  simpler  scheme  pre- 
viously given. 

2.  Use  of  the  Predicables. — The  accurate  and  intelligent 
observer  must  consciously  or  unconsciously  make  use  of 
some  such  scheme  in  order  to  make  his  observations  intelli- 
gent and  complete  ;  otherwise  he  will  never  know  when  he 
has  learned  the  most  important  facts  in  any  given  case,  nor 
when  he  has  learned  all  the  main  facts. 

The  scheme  will  decide  the  general  questions  to  be  asked 
when  attention  is  called  to  any  object  of  knowledge. 

1st.  What  is  it  in  its  substance— spiritual  or  material  ?  This  will  bring  out 
what  is  included  under  Aristotle's  category  of  substance. 

2d.  What  are  its  properties  of  quality  ?  This  will  embrace  Aristotle's  cate- 
gory of  quality. 

3d.  What  are  its  properties  of  action?  This  will  embrace  Aristotle's  catego- 
ries of  action  and  passion. 

4th.  What  are  its  properties  of  condition  ?  This  will  take  in  Aristotle's  cate- 
gories of  time,  place,  Quantity,  and  posture. 

5th.  What  are  its  properties  of  relation?  This  will  include  Aristotle's  cate- 
gories of  relation  and  possession. 

Topic  Second.  Observation  of  Things  Predicable. —  The 

practical  work  of  observation  lies  at  the  foundation  of  cor- 


THE   FORMATION    OF    CONCEPTIONS.         31 

rect  thinking,  since  such  thinking  must  depend  upon  first 
ascertaining  the  exact  facts  about  which  it  is  to  be  done. 
The  tendency  is  to  careless  and  superficial  observation.  Per- 
haps more  errors  in  science  arise  from  want  of  proper  obser- 
vation of  facts  than  from  any  other  source.  Hence  the  neces- 
sity of  securing,  in  the  earlier  stages  of  training,  the  careful 
study  and  diligent  practice  of  the  processes  and  rules  of 
exact  observation. 

I.  Processes  and  Products  of  Observation  in  General. 

Whately  styles  the  operation  of  the  mind,  in  contem- 
plating any  object,  simple  apprehension.  It  is  often  called 
intuition,  or  immediate  knowledge.  The  result  of  this 
operation  may  be  called  the  simple  notion.  This  notion 
may  take  various  forms,  from  that  of  the  vaguest  percept 
to  that  of  the  complete,  concrete  thing. 

In  beginning  the  work  of  observation  we  apprehend  ob- 
jects, whether  material  or  mental,  with  various  properties 
or  parts.  We  perceive  a  tree  with  its  trunk,  branches,  and 
leaves,  with  their  forms,  colors,  qualities,  etc.  We  thus 
gain  what  is  called  a  percept  of  the  tree.  We  may  subse- 
quently give  special  attention  to  any  particular  part  or 
property  of  the  tree,  as  its  height,  or  color,  or  firmness  of 
texture.  This  is  called  abstraction,  or  the  drawing  away 
of  a  part  or  property  from  the  concrete  whole.  The  result 
is  an  abstract,  or  abstract  notion,  of  these  parts  or  attri- 
butes, of  height,  color,  etc.  The  most  important  element  in 
accurate  observation  is  mental  analysis,  in  which  the  atten- 
tion is  voluntarily  turned  to  particular  parts  or  properties 
of  any  object  of  knowledge.  This  process  of  mental  sepa- 
ration is  continued  until  many  constituent  parts  of  the 
object  are  brought  out.  In  examining  material  objects, 
these  parts  may  evidently  be  regarded  either  as  spacial 
parts  or  as  attribute  parts.  The  first  point  of  view  leads 
to  what  is  called  physical  partition,  the  second  to  mental 
analysis  proper. 


32  PRACTICAL   LOGIC. 

Physical  partition  is  the  simplest  form  of  mental  analysis.  The 
analysis  of  tree  into  roots,  trunk,  branches,  leaves,  brings  out  the 
spacial  parts.  Such  partition  is  of  special  service  in  the  earlier  stages 
of  mental  training. 

Praxis. — Name  in  an  orderly  manner  the  parts  of  the  following 
objects:  1.  A  peach.  2.  A  piano.  3.  A  ship.  4.  A  book.  5.  A  house. 
6.  A  landscape.  7.  A  mountain  view.  8.  A  telephone.  9.  A  telescope. 
10.  A  locomotive. 

Mental  analysis  proper,  the  more  important  form  of  observation, 
deals  with  attributes  rather  than  with  spacial  parts.  It  belongs  to  a 
more  advanced  stage  of  mental  training.  Water  may  thus  be  ana- 
lyzed in  thought  into  the  separate  properties  named  weight,  liquid- 
ity, transparency,  refracting  power,  solvent  power.  A  dime  may  be 
analyzed  into  the  attributes  or  parts,  material  substance,  heavy, 
round,  small,  white,  coin. 

Note.— It  will  be  obvious  that  chemical  analysis,  involving  intricate  proc- 
esses of  thought,  belongs  to  a  different  range  of  mental  activity.  It  would 
bring  out  of  water  its  chemical  components,  oxygen  and  hydrogen,  and  out 
of  a  gold  dollar  its  chemical  components,  gold  and  the  alloy  of  silver  and 
copper. 

The  result  of  the  careful  application  of  these  processes 
of  abstraction  and  mental  analysis  is  the  notion  of  the  com- 
plete concrete  object,  or  thing1,  which,  according  to  Horn 
Tooke,  is  the  same  as  think,  a  thing  being  what  one  thing- 
eth  or  thinketh. 

Praxis. — Analyze  and  describe  in  an  orderly  way  the  following 
objects :  1.  A  diamond.  2.  A  gold  dollar.  3.  A  painting.  4.  A  piece 
of  wood.  5.  A  flower.  6.  A  rose.  7.  A  forest.  8.  A  sunset  at  sea. 
9.  A  church  service.  10.  An  act  of  memory. 

II.  Exact  or  Scientific  Observation  and  its  Rules. 

The  general  and  superficial  observation  thus  far  consid- 
ered, however  well  it  may  serve  the  purposes  of  common 
life,  is  insufficient  for  the  purposes  of  accurate  thinking. 
Scientific  observation  must  be  made  accurate  and  exact  by 
intelligent  conformity  to  certain  rules,  and  must  be  made 
complete  by  careful  use  of  the  scheme  of  things  knowable. 

1.  The  Rules  of  Observation,  which  need  to  be  grasped 
and  practised  in  order  to  reach  the  best  results,  are  three. 


THE   FORMATION    OF   CONCEPTIONS.        33 

They  are  substantially  Hamilton's  Laws  of  Integrity,  Par- 
cimony,  and  Harmony. 

Rule  1st.  Observe  all  the  essential  facts,  parts,  or  proper- 
ties in  any  given  case. 

Rule  2d.  Admit  no  fact,  part,  or  property  that  does  not 
belong  to  the  case  in  hand. 

Rule  3d.  Avoid  all  delusive  mixtures  of  inference  with 
the  facts  of  observation. 

Rule  1st  is  needed  to  guard  against  the  common  fault  of  incomplete 
observation.  Through  the  careless  use  of  the  powers,  or  the  holding 
of  some  false  theory,  or  the  blinding  influence  of  prejudice,  men  are 
liable  not  to  see  all  the  facts.  The  honest  observer  should  see  to  it 
that  none  of  these  things  stand  in  the  way  of  completeness  or  integ- 
rity of  observation.  Rule  2d  is  intended  to  guard  against  the  danger 
of  receiving  as  facts  things  that  are  not  such,  and  of  receiving  as  facts 
of  the  region  under  observation  things  which  belong  to  some  other 
sphere  of  facts.  This  danger  arises  in  the  same  way  as  the  preceding. 
Rule  3d  is  to  guard  against  the  introduction  of  unsound  or  irrelevant 
inferences  among  the  facts  of  observation.  The  sources  of  this  danger 
are  the  same  as  the  preceding.  Here  is  the  fruitful  source  of  much  of 
the  scientific  and  philosophic  error  in  all  ages. 

2.  Scientific  Observation,  in  order  to  the  best  results, 
while  conforming  to  these  rules,  must  make  intelligent  use 
of  the  categories.  The  observer  must  make  use  of  the 
questions,  already  given  in  connection  with  the  scheme,  in 
order  to  bring  out  the  facts  of  all  kinds. 

The  character  of  this  observation  will  appear  more  fully  in  the  later 
stages  of  the  study  of  Logic.  The  mode  of  using  the  scheme  may 
here  be  cursorily  illustrated,  and  the  main  things  in  the  process  sug- 
gested, by  the  observation  of  a  white-oak  tree  in  the  school-yard  or 
campus.  Question  first  will  bring  out  the  fact  of  material  substance 
or  constitution.  Question  second  will  give  the  facts  of  extension,  of 
organization,  of  life,  and  of  unity  of  structure  and  plan  in  the  tree, 
the  facts  of  cupule-bearing  and  half-covered  fruit,  and  the  other  facts 
peculiar  to  the  white-oak.  Question  third  will  furnish  the  facts  of 
growth,  of  resisting  violence,  of  counteracting  pressure,  etc.  Question 
fourth  will  lead  to  the  facts  concerning  the  height,  size,  shape,  habitat, 

C 


34  PRACTICAL    LOGIC. 

etc.,  of  the  tree,  and  those  concerning  its  time  of  planting,  length  of 
life,  periods  of  growth,  etc.  Question  fifth  will  direct  to  the  facts  con- 
cerning the  position  of  the  tree  with  reference  to  the  school-building, 
to  other  trees  and  objects  on  the  grounds,  to  other  trees  belonging  to 
the  class,  oak,  to  the  industrial  arts  in  which  its  wood  is  used,  etc. 

Praxis. — Observe  systematically  and  describe  carefully  the  following 
objects:  1.  An  inkstand  upon  the  writing-desk.  2.  A  clock  upon  the 
mantel-piece.  3.  A  student's  lamp  upon  the  table.  4.  A  Worcester's 
Dictionary  in  the  library-case.  5.  A  stove  in  the  room.  6.  A  ship  at 
sea.  7.  Jupiter  as  the  evening  star.  8.  The  centre-table  in  the  library. 
9.  The  feeling  of  home-sickness  in  the  student.  10.  The  contemplation 
of  Church's  Niagara. 

Note.— The  teacher  will  do  well  to  use  as  an  adjunct  some  such  work  as  the 
little  Manual,  published  by  Eldredge  &  Brother,  entitled  "  The  Cultivation  of 
the  Senses."  This  will  prepare  the  way  for  the  application  of  the  right  princi- 
ples to  the  more  difficult  work  of  introspection  and  analysis  of  mental  objects. 


Section  II,— Conception  Proper, 

Conception  proper  is  the  first  essential  element  in  the 
first  Form  of  Thought.  The  work  of  Observation  makes 
ready  the  material  for  it;  Conception  proper  begins  the 
work  of  comparing  that  material,  arriving  at  the  thought- 
connections,  and  gathering  up  and  combining  the  results  in 
a  thought. 

Topic  First.— The  Process  of  Concept-Forming. 

Definition. — Conception  proper  is  the  mental  process  of 
fixing  upon  resembling  parts,  marks,  or  properties  of  objects, 
and  grasping  them  singly  or  together  as  attribute  thoughts 
or  concepts. 

This  element  of  conception  always  involves  a  comparison  of  two  or 
more  objects  of  knowledge,  and  has  more  or  less  direct  reference  to 
the  process  of  classification  by  similar  properties.  The  concept  may, 
indeed,  be  said  to  be  formed  for  the  purpose  of  being  used  to  classify 
objects,  and  this  gives  it  its  chief  value.  There  is  need,  therefore,  of 
considering  two  things :  first,  the  gathering  of  similars  by  comparison ; 
second,  the  grasping  of  similars  in  thought  by  conception. 


THE   FORMATION    OF   CONCEPTIONS.        35 

I.  The  Gathering  of  Similars  by  Comparison. 

Comparison  in  the  formation  of  concepts  proper  begins 
with  the  work  of  fixing  upon  similar  properties.  Observ- 
ing objects  side  by  side,  we  note  and  affirm  differences  and 
resemblances,  and  then  fix  upon  and  abstract  the  resem- 
blances or  properties  common  to  the  objects. 

1.  The  simplest  connecting  act  in  thought  is  in  finding 
a  single  point  of  resemblance,  and  withdrawing,  or  abstract- 
ing, this  from  the  points  of  difference. 

E.g.,  water  has  materiality,  weight,  liquidity,  refracting  power, 
solvent  power,  transparency,  etc.  A  dime  has  materiality,  weight, 
whiteness,  hardness,  malleability,  roundness,  smallness,  the  stamp  of 
a  coin,  etc.  Air  has  materiality,  fluidity,  elasticity,  invisibility,  etc. 
Examining  these  three  objects  side  by  side,  they  are  all  found  to  have 
in  common  materiality.  They  resemble  each  other  in  this  point,  or,  in 
other  words,  this  is  a  characteristic  common  to  them  all. 

2.  A  more  important  connecting  act  in  this  first  stage  of 
thought  is  that  of  finding  and  seizing  upon  several  or  all 
the  points  of  similarity  in  the  objects  compared. 

It  will  readily  be  seen  that  the  same  objects  may  be  ob- 
served from  different  points  of  view.  A  gold  or  silver  coin 
may  be  observed  as  a  substance  having  essential  attributes 
of  its  own,  or  as  a  piece  of  money  used  in  the  work  of  com- 
mercial exchange.  The  observer  should  first  fix  upon  his 
point  of  view,  and  then  seek  the  resemblances  from  that 
point  of  view. 

Considered  as  a  substance,  a  sovereign  is  material,  of  yellow  color, 
extremely  malleable,  of  circular  shape,  nineteen  times  heavier  than 
water,  etc.  As  a  piece  of  money  it  is  of  the  metal  gold,  of  compara- 
tively high  value,  being  worth  five  dollars,  of  the  kind  which  is  the 
standard  of  values  in  most  countries,  a  coin,  etc.  Considered  as  a 
substance,  a  silver  dollar  is  material,  of  white  color,  moderately  mal- 
leable, of  circular  shape,  ten  times  heavier  than  water,  etc.  As  a 
piece  of  money  it  is  a  coin,  fashioned  of  the  metal  silver,  of  moderately 
high  value,  being  worth  one  hundred  cents,  etc.  Treating  the  gold 
and  silver  coins  as  substances  merely,  they  resemble  each  other  in 


36  PRACTICAL    LOGIC. 

being  material,  having  color,  being  malleable,  having  circular  shape, 
being  of  high  specific  gravity,  etc.  These  are  the  resembling  or 
common  properties  or  parts.  Treating  them  as  pieces  of  money,  they 
resemble  each  other  in  being  coins,  composed  of  metal  shaped  into 
circular  form  and  valuable  for  the  purposes  of  exchange. 

3.  The  most  important  connecting  act  in  this  stage  of 
thought  is  that  of  finding  and  fixing  upon  the  essential 
points  of  similarity  in  the  objects  compared.  Scientific 
thinking,  as  will  be  seen  further  on,  must  fix  mainly  upon 
the  essential  points  of  resemblance,  rather  than  upon  the 
non-essential. 

Praxis. — State,  concerning  the  properties  of  the  following  objects, 
whether  they  are  intrinsic  or  extrinsic ;  whether  essential  or  non- 
essential;  whether  properties  of  quality,  action,  condition,  or  relation : 
1.  Of  George  Washington, — born  in  Virginia  in  1732,  studied  mathe- 
matics under  a  private  instructor,  tall,  wise,  just,  brave,  president,  led 
the  armies  of  his  country,  the  friend  of  Hamilton,  the  father  of  his 
country,  died  in  1799.  2.  Of  Great  Britain, — populous,  fertile,  insu- 
lar, powerful,  manufacturing,  agricultural,  commercial,  philanthropic, 
missionary,  kingdom,  colonizing,  literary,  modern,  small,  nation. 

Compare  the  following  objects,  fixing  upon  some  resembling  prop- 
erty, and  stating  to  what  class  of  properties  it  belongs :  1.  Snow,  light, 
chalk,  lime.  2.  Book,  parchment  roll,  Kosetta  stone,  paper  manu- 
script. 3.  Oak-tree,  rose,  elephant,  man.  4.  Memory,  argument,  fence, 
watch,  world. 

Compare  the  following  objects,  fixing  upon  the  resembling  proper- 
ties, and  stating  to  what  class  they  belong :  1.  Wood,  coke,  charcoal, 
bituminous  coal.  2.  Plumbago,  charcoal,  diamond.  3.  Star,  student's 
lamp,  sun.  4.  Tree,  carriage,  watch,  poem.  5.  Poem,  painting,  statue, 
anthem,  temple.  6.  Triangle,  polygon,  dodecahedron,  globe. 

Note.— The  teacher  may,  with  great  profit  to  the  student,  devote  much  time 
to  the  processes  of  Observation  and  Comparison.  They  lie  at  the  very  basis  of 
correct  thinking,  so  that  their  importance  cannot  well  be  over-estimated. 

II.  The  Grasping  of  Similars  by  Conception, 

The  work  of  observation  and  comparison  up  to  the  pres- 
ent point  has  only  brought  out  common  attributes  without 
fixing  them  in  a  thought  binding  them  together  into  logical 


THE   FORMATION    OF    CONCEPTIONS.         37 

unity.  The  attributes  of  the  sovereign  as  money  are  named 
each  by  itself.  The  work  of  conception  brings  together 
all  these  attributes  into  one  thought,  which,  as  being  the 
product  of  conception,  is  called  a  concept,  or  attribute- 
thought.  This  concept,  which  is  named  sovereign  (in  accord- 
ance with  the  laws  of  naming  to  be  considered  under  Section 
Fourth)  embraces  in  itself  the  characteristics — coin,  fash- 
ioned of  the  metal  gold,  of  comparatively  high  value,  being 
worth  five  dollars,  of  the  kind  which  is  the  standard  of 
values  in  most  countries,  etc. 

The  value  of  the  product  of  thought  reached  by  the 
process  of  grasping  together  properties  will  depend  upon 
the  method  and  principles  followed. 

1.  It  is  obvious  that  any  of  the  kinds  of  properties 
already  considered  may  be  fixed  upon  and  embodied  in  the 
concept  or  attribute-thought,  and  that  this  may  be  done  in 
various  ways. 

a.  A  single  property  of  any  kind  may  be  fixed  upon,  in  which  case 
the  result  may  be  looked  upon  as  a  simple  concept,  although  the 
mental  act  is  one  of  simple  grasping,  and  not  of  grasping  together. 

b.  The  properties  of  any  particular  object  may  be  grasped  together, 
without  special  attention  to  other  objects,  or  to  the  principle  of  simi- 
larity.     This  may  also  be  regarded  as  an  unapplied  concept,  which 
may  be  applied  later  to  similar  objects  in  the  work  of  classification. 

c.  The  similar  properties  of  various  objects  may  be  grasped  together, 
keeping  in  view  the  principle  of  similarity.    This  is  the  concept  in  the 
strictest  sense. 

2.  The  Rules  which  must  govern  concept-forming,  if  the 
best  results  are  to  be  reached,  may  be  reduced  to  two. 

Rule  1st. — In  order  to  the  best  thought,  essential  prop- 
erties should  be  grasped  in  preference  to  others. 

The  loose  thinking  of  common  life  is  characterized  by  its  seizing 
upon  non-essential  properties.  In  observing  an  individual  man  the 
separable  accident  of  wearing  broadcloth  may  be  observed,  abstracted, 
and  embodied  in  the  concept  broadcloth-wearing.  Such  a  concept 
brings  out  nothing  essential  to  man.  Scientific  thinking,  on  the  other 
4 


38  PRACTICAL    LOGIC. 

hand,  fixes  chiefly  upon  essential  properties,  so  that  it  embodies  the 
very  nature  of  the  objects  of  thought.  In  observing  a  man,  it  fixes 
upon  the  animal  and  rational  properties  which  make  him  what  he  is, 
and  embodies  these  in  the  concept  man,  or  humanity.  The  products 
of  scientific  thinking  will  be  found  of  the  utmost  value  in  the  work 
of  classifying  objects. 

Rule  2d. — In  order  to  the  best,  the  only  adequate,  thought 
in  this  form,  all  the  essential  properties  should,  so  far  as 
possible,  be  grasped. 

It  is  obvious  that  any  number  of  abstractions  may  be  drawn  from 
any  object.  Strictly  speaking,  we  can  never  be  certain  that  all  the 
possible  properties  have  been  abstracted.  There  may  always  remain 
innumerable  unobserved  or  undetected  properties.  But  ordinarily  all 
the  essential  properties  may  be  more  or  less  clearly  detected  and 
grasped,  and  the  perfection  of  the  concept  as  a  group  of  properties 
will  depend  upon  the  completeness  with  which  it  takes  in  the  essence 
of  the  object  of  thought. 

Observing  carefully  an  animal,  the  properties  of  organized  being,  of 
life,  of  sentiency,  and  of  voluntary  motion,  are  fixed  upon  as  essential 
properties.  These  are  all  embodied  in  the  concept,  animal.  If  but 
one  of  these  sets  of  properties  should  be  embodied,  the  concept  would 
be  of  comparatively  little  value.  Observing  some  virtuous  act,  as  the 
Prophet  Daniel's  act  of  praying  to  the  true  God  notwithstanding  the 
prohibitory  decree  of  the  king,  the  characteristics,  conformity  to  the 
law  of  right,  and  intelligent,  intentional  action,  are  fixed  upon  and 
embodied  in  the  concept  virtue,  or  virtuousness.  If  any  one  of  these 
essential  characteristics  is  omitted  in  our  conception  of  virtue,  the 
thought  will  be  incomplete  and  of  little  value  scientifically. 

Praxis. — Gather  up  into  concepts  the  similar  properties  of  the  fol- 
lowing groups  of  objects,  stating  the  kind  of  property  in  each  case: 
1.  A  piece  of  crayon,  a  chair,  a  lamp,  a  book,  a  tree,  a  stone.  2.  A 
man,  an  eagle,  a  lion,  a  serpent.  3.  A  horse,  a  tiger,  an  elephant,  a 
lap-dog.  4.  A  cat,  a  leopard,  a  hyena.  5.  A  vulture,  a  hawk,  a 
falcon.  6.  Love,  patience,  joy,  gratitude.  7.  Faith,  hope,  charity. 

8.  Cathedral  of  Milan,  Madonna  of  Raphael,  Paradise  Lost  of  Milton. 

9.  Great  Britain,  United  States,  Germany. 

Topic  Second,— The  Product  of  Concept-Forming. 

The  product  of  gathering  up  the  abstracted  properties  of 


THE    FORMATION    OF    CONCEPTIONS.         39 

objects  in  thought  is  a  thought  property  or  group  of  proper- 
ties. It  would  be  appropriately  named  a  notion  (from  notce, 
marks,  characteristics),  if  that  word  were  not  used  in  such 
loose  and  varied  senses.  Concept  proper  is,  perhaps,  the  best 
name.  But  whether  spoken  of  as  notion,  concept  proper,  or 
attribute  thought,  the  essential  thing  in  it  is  always  the 
grasping  in  thought  of  certain  observed  properties  of  objects. 

The  properties  contained  in  any  concept  make  up  its  con- 
tent. The  same  thing  has  also  been  denoted  by  internal 
quantity,  intension,  comprehension,  depth,  marks,  etc.  The 
content  of  the  concept  man  is  made  up  of  animal  and 
rational  properties.  The  content  of  triangle  is  plane  figure, 
three-sided,  rectilineal. 

In  connection  with  concepts  proper,  Logic  gives  promi- 
nence to  their  reciprocal  relations  by  content.  These  rela- 
tions may  be  considered  from  two  points  of  view  :  first,  that 
of  identity,  and,  second,  that  of  congruity. 

1.  Compared   by   content,   concepts   proper   are   distin- 
guished as  identical  and  different.     They  are  — 

1st.  Identical,  when  they  coincide  in  their  marks,  or  comprise  the 
same  properties.  Identity  is  either  absolute  or  relative.  Absolute 
identity,  or  sameness,  does  not  strictly  exist  between  concepts,  but  rela- 
tive identity,  or  similarity,  does  exist.  The  terms  of  a  complete  defi- 
nition approach  most  nearly  to  absolute  identity,  both  comprising  the 
same  marks  or  properties,  e.g.,  "  Body  is  extended  substance." 

2d.  Different,  when  they  do  not  comprise  the  same  properties.  Dif- 
ference is  again  either  absolute  or  relative. 

2.  Compared  by  content,  concepts  proper  are  also  divided 
by  logicians  into  congruent  and  conflictive. 

1st.  Congruent  notions  are  such  as  may  be  connected  in  thought 
with  the  same  object,  as  good,  wise,  powerful,  etc. 

2d.  Conflictive  notions  are  such  as  may  not  be  connected  in  thought. 
Conflictive  opposition  is  either  contradictory  or  contrary.  Immediate 
or  contradictory  opposites  are  "  directly,  immediately,  and  absolutely 
repugnant"  to  each  other,  as  exemplified  in  yellow,  not-yellow  ;  walk- 
ing, not-walking.  Of  these  conflictives  there  can  be  two  only,  and 
one  of  them  must  be  true.  In  contrary  opposition,  on  the  other  hand, 


PRACTICAL    LOGIC. 


more  than  two  conflictive  characters  are  possible,  as  yellow,  blue,  red, 
etc. ;  sitting,  standing,  lying,  etc.  If  one  of  these  be  not  predicated  of 
any  person,  it  does  not  follow  that  any  one  other  must  be.  Thus, 
though  I  cannot  at  once  sit  and  stand,  yet  I  may  be  neither  sitting 
nor  standing, — I  may  lie ;  but  I  must  either  sit  or  not  sit ;  I  must 
either  stand  or  not  stand,  etc. 

These  relations  of  concepts  by  content  may  be  represented  to  the 
eye  by  diagram.  Squares  may  be  used  to  represent  the  sphere  or  con- 
tent of  concepts  and  also  the  objects  of  which  they  may  or  may  not 
be  predicated.  The  overlapping  parts  of  the  double  squares  and  the 
dotted  lines  indicate  the  partial  coincidence  of  the  properties.  The 
sign  plus  (-(-)  may  indicate  congruence,  the  sign  minus  ( — )  confliction. 


or 


1.  Identity, 


2.  Difference, 


Absolute,  or 
Sameness, 

Relative,  or 
Similarity, 


Absolute, 


Relative, 


Humanity  and 

Rational  I    and 

Animality.  '  "•  -"-• 


Affection 

and 
Desire. 
Common  Element  =  Emotion. 

Spirituality 

and 
Materiality. 


Touching  in  Being. 


Science 
and 
Art. 


Common  Element  =  System  of  Truth. 


1.  Congruence, 


Good, 
Wise 
Just, 


in  Moses. 


2.  Conflic- 
tion, 


Contradictory 
Opposition, 

Contrary  Op- 
position, 


Living 
and 


Not-living.  J         L  — 


I  with 
f  Paul. 


Red, 
Blue, 
Green, 


and 


R 

I- 


THE   FORMATION    OF    CONCEPTIONS.        41 

Praxis. — State  and  illustrate  by  diagram  the  relation  by  content 
of  the  following  concepts:  1.  Running,  lying.  2.  Blue,  not-blue. 
3.  White,  black.  4.  Money,  memory.  5.  Learning,  virtue.  6.  Saint, 
sinner.  7.  Grace,  unmerited  favor.  8.  Yellow,  blue,  red.  9.  Walk- 
ing, standing,  sitting,  running.  10.  Wealth,  poverty.  11.  Beauty, 
virtue.  12.  Old,  middle-aged,  young.  13.  Tall,  short. 

Give  five  examples  of  each  of  the  following  relations  of  concepts  by 
content:  1.  Identity  absolute.  2.  Identity  relative.  3.  Difference 
absolute.  4.  Difference  relative.  5.  Congruence.  6.  Contradictory 
opposition.  7.  Contrary  opposition. 

Section  III,— Classification, 

The  second  essential  element  of  conception,  in  the  wide 
sense,  may  be  defined  as  grasping  in  one  thought,  called  a 
class,  all  the  objects  to  which  the  attributes  included  in 
any  concept  or  notion  are  common.  Hence  the  process  is 
called  classification.  From  another  point  of  view  it  may 
be  defined  as  extending  the  application  of  the  content  of  a 
concept  or  notion  to  all  the  objects  to  which  it  is  applicable. 
Hence  the  process  is  also  called  generalization. 

A  dime  has  the  property  of  roundness.  When  we  extend  the  appli- 
cation of  this  property  to  all  bodies  that  possess  it,  and  so  connect 
them  all  with  dime  into  one  thought,  the  result  is  the  class,  round 
bodies.  A  dime  has  the  property  of  whiteness.  When  we  extend  the 
application  of  this  property  in  the  same  manner  as  before,  the  result 
is  the  class,  white  bodies.  Making  use  of  both  round  and  white,  the 
result  is  the  class,  round,  white  bodies.  Classifying  by  the  mark, 
stamped  as  coin,  the  result  is  the  class  of  coins. 

It  is  thus  evident  that  the  work  of  classification  is  simply  the  gen- 
eral application  of  one  or  more  properties  of  a  concept  to  objects.  The 
resemblance  of  properties  or  attributes  furnishes  the  key  to  the  work. 
If  bodies  had  no  differences,  there  would  be  but  one  great,  monotonous 
mass  of  existing  things ;  if  they  had  no  resemblances,  no  two  could  be 
brought  together  into  a  group,  and  there  would  be  no  possibility  of 
thought.  Classification  is  possible  because  objects  have  both  different 
and  resembling  properties. 

Topic  First— Process  of  Classification. 

Classes  may  either  be  considered  singly,  or  in  systems 


42  PRACTICAL    LOGIC. 

or   combinations.      Hence    the    ordinary    distinctions   and 
rules. 

1.  In  forming  single  classes,  it  is  obvious  that  the  thinker 
may  make  use  of  accidental,  peculiar,  or  essential  proper- 
ties.    In  order  to  reach  the  most  valuable  scientific  results, 
classification   should    keep   in   view   the   most    important 
properties. 

Rule. —  Classify  by  essential  properties  rather  than  by 
non-essential. 

Gold  might  be  classified,  by  the  property  of  color,  with  yellow 
objects  ;  silver  in  the  same  way  with  white  objects.  Such  a  classifica- 
tion would,  however,  be  of  no  scientific  value.  Taking  the  resembling 
essential  properties  of  the  two:  (1),  they  are  elements  or  simple  sub- 
stances; (2),  they  possess  metallic  lustre;  (3),  they  are  good  con- 
ductors of  heat  and  electricity, — they  may  be  classified  with  other 
objects  having  like  properties,  as  metals.  Such  classification  is  of  sci- 
entific value. 

Praxis. — Classify  each  of  the  following  with  like  objects  by  various 
non-essential  and  essential  properties :  1.  Porter's  "  Human  Intellect." 
2.  A  comet.  3.  The  north  star.  4.  The  Temple  of  Solomon.  5.  The 
Parthenon.  6.  The  Washington  Monument.  7.  The  Mississippi  River. 
8.  The  Mer  de  Glace.  9.  Mount  Vesuvius.  10.  Victoria  of  England. 
11.  Ulysses  S.  Grant.  12.  Jefferson  Davis.  13.  Moses.  14.  Jesus. 

2.  Objects  of  knowledge  are  so  related  that  they  may  be 
arranged  in  systems  of  classes.    Such  classification  requires 
the  application  to  classes  of  the  process  used  in  forming 
single  classes,  while  keeping  in  view  the  wider  relations  of 
things.     It  is  a  successive  classification  of  classes. 

Rule. — Classify  the  lower  classes  under  higher  by  fixing 
upon  properties  common  to  the  lower. 

Certain  figures  are  classified,  by  the  number  and  relation  of  their 
straight  sides,  as  triangles,  squares,  parallelograms,  polygons,  etc.  All 
these  classes  have  the  common  characteristic,  being  bounded  by  straight 
lines,  and  may,  therefore,  be  classed  as  rectilinear  figures.  Certain  other 
figures  are  classified,  by  the  various  character  of  their  curved  boun- 
dary-lines, as  circles,  ellipses,  parabolas,  hyperbolas,  etc.  All  these 


THE   FORMATION   OF   CONCEPTIONS.        43 

classes  have  the  common  characteristic,  being  bounded  by  curved  lines, 
and  may,  therefore,  be  classed  as  curvilinear  figures.  Rectilinear  and 
curvilinear  figures  have,  as  a  common  characteristic,  plane  surface, 
and  may,  therefore,  be  classed  as  plane  figures.  Certain  other  figures 
are  classed,  by  the  character  of  their  bounding  surfaces,  as  tetrahe- 
drons, cubes,  parallelepipeds,  etc.  They  are  in  common  bounded  by 
plane  surfaces,  and  may,  therefore,  be  classed  as  plane  solids.  Certain 
other  figures  are  classed,  by  the  character  of  their  bounding  surfaces, 
as  spheres,  cones,  paraboloids,  etc.  They  are  in  common  bounded  by 
curved  surfaces,  and  may,  therefore,  be  classed  as  curved  solids.  Both 
plane  and  curved  solids  have  in  common,  solidity,  and  may,  therefore, 
be  classed  as  solid  figures.  Plane  figures  and  solid  figures  have  in 
common,  extension,  which  is  the  subject-matter  of  Geometry,  and  may, 
therefore,  all  be  classed  as  geometrical  figures.  The  result  is  a  System 
of  Classes : 


Triangles, 

Squares, 

Rectilinear 

Polygons, 

Figures. 

. 

etc. 

1 

Circles, 

Plane  Figures.  • 

o 

Ellipses, 

Curvilinear 

8 

Parabolas, 
Hyperbolas, 
etc. 

Figures. 

Geometrical 

<D 

Tetrahedrons, 

Figures. 

3 

Cubes, 

Plane 

1 

Parallelepipeds, 

Solids. 

| 

etc. 

Solid  Figures.       J 

Spheres, 

Cones, 

Curved 

Paraboloids, 

'  Solids. 

etc. 

Such  systems  are  found  on  the  most  extensive  scale  in  the  classifi- 
cation of  animals  and  plants,  in  Zoology  and  Botany.  Exercises  in 
forming  systems  of  classes  may  be  drawn  from  these  sciences. 

Praxis.— Classify  the  following  collections  or  masses  of  objects  in 
single  classes  and  in  systems  of  classes:  1.  The  articles  in  a  school- 
room. 2.  The  objects  in  a  school  or  college  campus.  3.  The  struc- 


44  PRACTICAL    LOGIC. 

tures  in  New  York  city.  4.  The  objects  comprised  in  a  farm.  5.  The 
objects  embraced  in  a  Pennsylvania  landscape.  6.  The  objects  in  the 
heavens  as  revealed  by  a  powerful  telescope.  7.  The  operations  of  the 
human  soul.  8.  The  things  seen.  9.  The  things  unseen. 

Topic  Second. — Results  of  Classification. 

The  product  of  the  general  application  of  the  concept  to 
all  the  objects  to  which  it  is  common  is  a  thought-group,  or 
a  thought-system,  of  objects,  i.e.,  a  class  or  a  system  of 
classes. 

In  the  general  notion  as  class,  the  essential  thing  is 
always  the  grasping  together  of  individuals.  The  indi- 
viduals contained  in  any  such  general  notion  make  up  its 
extent.  The  extent  has  also  been  denoted  by  external  quan- 
tity, extension,  breadth,  etc. 

In  connection  with  the  class  notion  and  extent,  Logic 
gives  prominence  to  two  things :  first,  the  relations  of  gen- 
eral notions  as  classes  to  one  another  by  extent ;  second,  the 
reciprocal  relations  of  extent  and  content,  or  of  the  class 
and  the  concept  proper. 

I.  Relations  of  Classes  to  One  Another. 

1.  Compared  by  extent,  general  notions  as  classes  stand 
to  each  other  in  five  mutual  relations:  exclusion,  co-exten- 
sion, subordination,  co-ordination,  and  intersection. 

1st.  Exclusion. — One  class  excludes  another  when  no  part  of  the 
one  coincides  with  any  part  of  the  other;  e.g.,  horse  and  syllogism. 
No  horse  is  ever  a  syllogism,  and  vice  versa. 

2d.  Co-extension. — One  class  is  co-extensive  with  another  when  each 
includes  exactly  the  same  species ;  e.  g.,  living  being  and  organized 
being.  Using  life  as  including  plant  life,  every  living  being  is  an 
organized  being,  and  vice  versa. 

3d.  Subordination. — One  class  is  subordinate  to  another  (which  is 
called  the  superordinate)  when  the  former  is  included  in  the  latter  as  a 
part  of  it ;  e.  g.,  dog,  horse,  under  quadruped.  Every  dog  is  a  quad- 
ruped, as  is  also  every  horse. 

4th.  Co-ordination. — Two  or  more  classes  are  co-ordinate  when  they 
are  co-exclusive,  yet  all  immediately  comprehended  under  the  same 


THE   FORMATION   OF    CONCEPTIONS.         45 


higher  class ;  e.  g.,  dog,  horse,  while  immediately  subordinate  to  the 
higher  class,  quadruped,  are  co-exclusive  and,  therefore,  co-ordinate. 

5th.  Intersection. — Two  classes  intersect  each  other  when  each  is 
partially  included  in  the  other  ;  e.  g.,  rational  and  animal.  Some 
rational  beings  are  animals  and  some  are  not,  and  vice  versa. 

These  relations  may  be  symbolized  by  Euler's  circular 
notation,  in  which  the  extent  of  classes  is  represented  by 
circles,  and  the  relations  of  classes  by  the  relative  positions 
of  the  circles. 


fa 

§* 


1.  Exclusion. 

Horse,  syllogism. 

2.  Co-extension. 

Living  being,  organized  being. 

3.  Subordination. 

Quadruped,  horse. 

4.  Co-ordination. 

Quadruped,  lion,  horse. 

5.  Intersection. 

Rational  being,  animal. 


Starting  from  Inclusion,  other  logicians  divide  the  rela- 
tions of  classes  into  those  of  (1),  Inclusion,  embracing, 
(a),  Co-extension,  and  (b),  Subordination ;  (2),  Intersec- 
tion ;  (3),  Exclusion,  embracing,  (a),  Co-ordination,  and 
(b),  Non-co-ordination. 

2.  Special  Relations  arising  from  Classification. 

Out  of  classes  and  systems  of  classes  arise  various  logical 
distinctions  which,  as  they  occur  constantly  in  science  and 
philosophy,  in  the  writings  of  the  modern  as  well  as  ancient 
masters,  should  be  understood  by  the  student  who  expects 
to  read  and  think  for  himself. 


46  PRACTICAL    LOGIC. 

(1.)  The  simpler  forms  of  classification  give  rise  to  the 
distinctions  of  genus,  species,  differentia,  individual. 

In  any  series  of  higher  and  lower  classes,  each  higher  class  is  a 
genus  to  those  next  below  it.  Those  classes  next  below  the  genus  are 
its  species.  Caucasian,  Mongolian,  Malaysian,  Negro,  and  American 
Indian  are  species  of  the  genus,  man.  Or,  if  European  is  considered  as 
a  genus,  German,  Frenchman,  Englishman,  etc.,  are  the  species.  Dif- 
ferentia, or  specific  difference,  is  the  characteristic  or  property,  simple 
or  complex,  which  distinguishes  one  species  from  others  under  the 
same  genus.  Bed  is  the  differentia  of  red  rose,  or  that  which  distin- 
guishes it  from  white,  yellow,  and  other  species  of  the  genus,  rose.  An 
individual  is  one  of  the  single  objects  of  which  a  species  or  genus  is 
always  made  up.  It  is  only  capable  of  physical  or  mechanical  par- 
tition, and  can  never  be  a  genus.  Washington  and  Napoleon  are 
individuals. 

Note.— Species,  in  its  peculiar  use  in  Natural  History,  needs  to  be  carefully 
distinguished  from  species  in  Logic.  In  Natural  History,  species  means  only 
"such  a  class  of  animals  as  has,  or  might  have,  descended  from  a  single  origi- 
nal pair,  and  the  varieties  of  which  may  permanently  interpropagate  among 
themselves."  The  sub-species  are  named  varieties.  Greyhound,  spaniel,  ter- 
rier, bull-dog,  etc.,  are  varieties  of  the  species,  dog. 

(2.)  Systems  of  classes  give  rise  to  the  logical  distinc- 
tions of  summum  genus,  infima  species,  subaltern  genera 
and  species,  proximate  genera  and  species,  superordinates, 
subordinates,  co-ordinates,  and  disparates. 

The  highest  class  in  any  system  of  classes  is  known  as  summum 
genus ;  the  lowest  class,  which  can  never  be  a  genus,  as  infima  species. 
The  absolute  highest  genus  is  being,  which  includes  all  the  existences 
in  the  universe.  In  classifying  any  department  of  knowledge,  it  is 
usual,  however,  to  assume  and  start  from  some  relative  highest  genus. 
In  Botany,  this  genus  is  plant;  in  Zoology,  animal.  Subaltern  genera, 
or  sub-classes,  are  those  which  are  species  of  a  higher  genus.  Subal- 
tern species,  or  sub-species,  are  species  of  some  higher  species  consid- 
ered as  a  genus  to  those  lower  than  itself.  White  oak,  black  oak, 
scarlet  oak,  yellow  oak,  etc.,  are  subaltern  species  of  oak.  Oak  is  a 
species  of  the  genus,  mastwort,  or  cup-bearing  trees,  and  constitutes, 
with  chestnut,  beech,  hazel,  and  hornbeam,  the  subaltern  genera,  or 
sub-classes,  of  that  class. 

This  may  be  illustrated  by  the  following  tabular  example: 


THE   FORMATION    OF    CONCEPTIONS.         47 

Designations.  Glasses. 

Summum  Genus.  Being  or  Thing. 

Species  or  Subaltern  Genera.  Organic  (Inorganic). 

Intermediate  or  Sub-Species.  Animal  (Plant). 

Infima  Species.  Man  (Brute). 

Individuals.  Washington  (Other  Men). 

Genera  and  species,  which  are  next  to  each  other  in  order  of  ascent 
or  descent  in  any  system  of  classes,  are  known  as  proximate  genera 
and  species,  or  nearest  classes  and  species ;  as  animal  and  man,  in  the 
example  just  given.  The  higher  genus  in  relation  to  a  lower  is  called 
the  superordinate  genus,  or  next  in  rank  above ;  the  lower  in  relation 
to  the  higher,  the  subordinate,  or  next  in  rank  below.  The  species 
under  any  genus  are  co-ordinates,  or  of  equal  rank.  This  may  be 
illustrated  by  the  following  example  : 

Assumed  Highest  Genus, — Cup-bearing  Trees. 
Species.      Oak.       Chestnut.          Beech.  Hazel.       Hornbeam. 

S    f  Red,         American,      American,      American,     Ironwood, 
Spanish,         Red,  Beaked,        Hornbeam, 

Dwarf,  etc.  etc.  etc. 

etc. 

Oak,  chestnut,  etc.,  are  superordinates  with  reference  to  the  co- 
ordinate species  respectively  embraced  under  them.  The  co-ordinate 
species,  red,  white,  etc. ;  American,  Spanish,  etc.,  are  subordinates  to 
oak  and  chestnut  respectively,  and  these  last  to  the  higher  genus,  cup- 
bearing  trees,  which  embraces  also  beech,  hazel,  and  hornbeam.  Any 
one  of  these  co-ordinates,  considered  in  relation  to  a  higher  or  lower 
part  in  the  divisions  of  any  of  the  other  co-ordinates  in  the  system  of 
classes,  is  called  disparate.  Red  oak  as  compared  with  chestnut  is 
disparate. 

II.  Reciprocal  Relations  of  Concepts  and  Glasses. 

The  concept  and  class  notions  are  both  very  closely  con- 
nected with  one  another,  and  embodied  in  one  word.  From 
one  point  of  view  the  word  man  means  the  rational  and 
animal  properties  which  make  man  what  he  is.  It  has, 
therefore,  content  or  contained  properties.  From  another 
point  of  view  man  means  all  the  individuals  that  have  these 


48  PRACTICAL    LOGIC. 

common  properties,  or  all  mankind.  It  has,  therefore, 
extent  or  comprehended  objects.  The  Rule  expressing  the 
relation  of  content  and  extent  is,  that  as  the  content  in- 
creases the  extent  diminishes,  and  as  the  extent  increases 
the  content  diminishes. 

In  other  words,  the  greater  the  number  of  properties  in  a  concept, 
the  less  the  number  of  objects  that  have  all  these  properties  in  common, 
and  the  greater  the  number  of  objects  in  a  class,  the  less  the  number 
of  properties  common  to  them  all.  This  may  be  illustrated  by  the 
following  diagram  of  concept  and  class  in  content  and  extent : 

CONCEPT  CONTENT,  EXTENT, 

and  i.  e.,  the  properties  con-          i.  e.,  the  objects  embraced 

CLASS.  tained  in  the  concept.  in  the  class. 

Body.  Extended  substance.          Stone,  Plant,  Brute,  Man,  etc. 

Living  Body.     Body  with  life.  Plant,  Brute,  Man. 

Animal.  Body  with  life  and  sensation.  Brute,  Man. 

Man  |  Body  with  life,  sensation,  and  1  -^an 

i      reason.  J 

Washington,  f  Body  with  life>  sensation,  reason,  )        individual. 
(.      Father  of  his  country.  J 

From  this  diagram  it  is  apparent  that  the  concept,  body,  which  has, 
as  its  content,  only  extended  substance,  has  the  greatest  extent,  em- 
bracing stone,  plant,  brute,  man,  etc.,  while  the  lowest  concept,  man, 
which  has,  as  its  content,  extended  substance  with  life,  sensation,  and 
reason,  has  the  least  extent,  embracing  only  mankind.  Washington, 
with  still  broader  content,  has,  as  its  extent,  only  an  individual. 
Being,  the  concept  of  least  possible  content,  containing  simply  exist- 
ence, is  the  absolute  highest  class,  and  has  the  greatest  possible  extent, 
embracing  all  things  material  and  spiritual. 

Praxis. — Give  five  illustrations  of  each  of  the  following  relations 
of  classes:  1.  Exclusion.  2.  Co-extension.  3.  Subordination.  4.  Co- 
ordination. 5.  Intersection. 

State  and  illustrate,  by  diagram  and  by  circular  notation,  the  rela- 
tions of  the  classes:  I.Man,  horse.  2.  Dog,  ox,  alligator.  3.  Book, 
manuscript.  4.  Magazine,  daily  paper.  5.  Planet,  body  moving  round 
the  sun.  6.  Aryan,  European,  Frenchman.  7.  Faith,  hope,  love. 
8.  Affection,  desire.  9.  Man,  animal.  10.  Plant,  tree.  11.  House, 
barn.  12.  Botany,  Geology.  13.  Mathematics,  Astronomy. 

Illustrate  by  three  examples  each:   1.  Genus,  species,  differentia, 


THE   FORMATION    OF    CONCEPTIONS.         49 

individual.  2.  Highest  class,  lowest  species,  sub-class,  sub-species, 
superordinate,  subordinate,  co-ordinate,  disparate.  3.  The  varying 
relation  of  content  and  extent. 

Section  IV,— Denomination, 

When,  by  the  processes  of  conception,  concepts  and  classes 
have  been  formed,  they  need  to  be  embodied  in  language  in 
order  that  they  may  be  fixed  and  made  subject  to  recall  for 
further  use.  This  is  the  third  essential  element  in  Concep- 
tion. 

Topic  First. — The  Process  of  Naming. 

Language  is  the  expression  of  thoughts  by  means  of 
words  spoken  or  written.  It  is  the  medium  of  communi- 
cation between  men.  It  fixes  thoughts  which  would  other- 
wise be  vague,  or  fleeting,  or  confined  to  some  individual, 
and  makes  them  the  property  of  all.  It  thus  greatly  facili- 
tates the  progress  of  our  thinking.  In  short,  while  it  is 
true  that  some  of  our  processes  of  thought  may  be  carried 
on  without  any  language,  it  is  nevertheless  true  that  with- 
out it  thought  would  practically  cease,  while  communica- 
tion would  become  impossible. 

I.  Modes  of  Naming. 

In  giving  names  to  our  conceptions,  the  aim  should  be  to 
embody  them  as  perfectly  as  possible  and  bring  them  as 
fully  as  may  be  under  the  recall  and  control  of  ourselves 
and  others.  It  is  evident  that  this  aim  is  not  always  kept 
in  view.  Things  are  named  in  various  ways,  and  the  names, 
judged  by  the  mode  in  which  they  are  given,  are  oftener 
non-logical  than  logical. 

1.  The  name  is  sometimes  purely  arbitrary.  This  is  often  the  case 
with  the  strictly  proper  name.  "  It  denotes  an  individual,  but  does 
not  indicate  or  imply  any  attribute  of  that  individual.  .  .  It  is  an 
unmeaning  mark  or  sign  which  we  connect  in  our  minds  with  an 
object,  so  that  when  this  sign  meets  our  eyes  or  ears  we  may  think  of 
5  D 


50  PRACTICAL    LOGIC. 

that  individual."     The  most  profane  of  men  may  be  named  Christo- 
pher, Christ-bearer. 

2.  The  name  is  sometimes  given  from  some  accidental  circumstance 
or  property.     In  proper  names  this  is  illustrated  by  such  Bible  names 
as  Moses,  drawn  out;  Isaac,  laughter.    In  common  or  class  names,  the 
same  process  is  illustrated  by  moon,  measurer;  planet,  wanderer;  vul- 
ture, flyer;  lord,  loaf -keeper. 

3.  The  name  sometimes  embodies  some  prominent  essential  property 
or  mark.      This  is  illustrated  by  such  words  as  sun,  shiner;  man, 
thinker;  animal,  breather;  barometer,  weight-measurer. 

4.  The  perfect  or  strictly  logical  name  aims  to  embody  as  completely 
as  possible  the  entire  essence  of  a  conception.      As  such  naming  is 
difficult  in  the  case  of  complex  conceptions,  it  is  usually  necessary  to 
fix  upon  some  prominent  essential  property,  in  accordance  with  the 
principle  already  given.     The  essential  marks  in  the  conception,  man, 
are  rational  and  animal,  but  the  Aryan  people  who  named  man  seized 
upon  the  essential  mark,  thought,  and  so  called  him  man,  i.  e.,  thinker. 

5.  Names,  as  languages  are  constituted,  are  often,  in  fact,  little  more 
than  mere  hints,  which  start  the  mind  on  its  work  of  interpretation. 
This  has  been  shown  by  Hamilton  to  be  one  of  the  necessities  of  lan- 
guage,— since,  unless  the  vocabulary  becomes  almost  infinite  so  as  to 
express  all  our  single  notions,  the  same  words  must  be  used  to  express 
a  multitude  of  thoughts,  more  or  less  differing  from  each  other.     See 
Hamilton's  Logic,  p.  437. 

II.  Rules  for  Naming. 

The  Rules  for  giving  names  to  our  conceptions  naturally 
arise  from  the  aim  in  naming. 

Rule  1st. — Name  a  conception  what  it  is. 

The  science  of  the  human  soul  should  be  named,  not  mental  philoso- 
phy, nor  intellectual  philosophy,  nor  metaphysics,  nor  philosophy,  but 
psychology. 

Rule  2d. — Make  the  name  self-interpreting  if  possible. 

A  name  is  notative  when  it  suggests  its  own  marks  (note),  and  thus 

»  becomes  self-interpreting.    It  is  symbolical  when  it  serves  as  a  symbol 

or  label  of  properties  or  marks  which  it  does  not  suggest.     Names 

should  be  notative,  if  possible,  in  order  to  give  the  mind  the  best  start 

in  its  work  of  interpretation.     It  is  a  fact  to  be  noted,  that  many 


THE  FORMATION   OF    CONCEPTIONS.         51 

names  which  were  originally  notative  have  lost  their  power  of  sug- 
gestion except  to  men  who  are  educated.  To  one  who  would  best 
understand  thought  as  expressed  in  English,  acquaintance  with  the 
languages  from  which  the  English  has  drawn  its  words  becomes  a  neces- 
sity. To  one  acquainted  with  Latin,  triangle,  quadruped,  biped,  become 
notative  and  self-interpreting.  To  one  having  the  mastery  of  Greek, 
democracy,  oligarchy,  oxygen,  mythology,  philosophy,  become  self- 
interpreting.  To  one  understanding  Anglo-Saxon,  lord,  wicked,  battle, 
war,  orchard,  become  self-interpreting.  To  one  versed  in  Philology 
and  History,  heathen,  villain,  church,  sincere,  saunter,  become  self- 
interpreting. 

Rule  3d, — Make  the  name  as  simple  as  possible. 

As  the  genius  of  our  language  is  Saxon,  let  the  preference  be  given 
to  Saxon,  and,  if  possible,  let  the  name  be  a  single  word.  Pierce  is 
better  than  penetrate ;  love  is  stronger  than  affection,  and  hate  than 
animosity  ;  working  is  more  forceful  than  operation.  Psychology,  as 
being  one  word,  is  better  than  intellectual  philosophy ;  arithmetic 
than  the  art  of  computation. 

Rule  4th. — In  naming  a  system  of  conceptions  or  classes, 
use  a  system  of  names. 

In  a  system  of  names  one  may  be  made  to  suggest  all  the  other 
names  and  thoughts.  Such  system  is  thus  of  immense  advantage, 
especially  in  the  various  Sciences.  In  .the  Natural  History  Sciences, 
which  deal  largely  with  classes,  a  system  of  distinctions  has  been 
adopted  by  which  the  precise  place  of  each  logical  genus  and  species 
in  the  great  system  of  classes  may  be  accurately  fixed.  In  Zoology, 
the  Animal  Kingdom  is  separated  by  Agassiz  into  Branches,  Classes, 
Orders,  Families,  Genera,  Species,  Varieties. 

Praxis. — Test  the  following  names  by  the  rules  for  naming,  stating 
whether  they  are  notative  or  symbolical:  1.  Intellectual  Philoso- 
phy, for  science  of  the  human  soul.  2.  Paternal  ancestor,  for  father. 
3.  Affection,  for  love.  4.  Sierra  Nevada  Mountains.  5.  Telegraph. 
6.  Geology.  7.  Geography.  8.  Academy.  9.  School  of  herring.  10.  Ac- 
cident. 11.  Blackboard.  12.  Candlestick.  13.  Ambition.  14.  Navy. 
15.  Book.  16.  Bible.  17.  Volume.  18.  Parchment.  19.  Paper. 
20.  Pen. 


52  PRACTICAL    LOGIC. 

Topic  Second. — Products  of  Naming. 

The  products  of  naming  concepts  and  classes  are  the 
various  kinds  of  terms  in  which  our  notions  are  embodied. 
The  divisions  are  based,  (1),  either  upon  something  in  the 
term  itself;  or  (2),  upon  something  in  the  relations  of 
terms. 

I.  Kinds  of  Terms  arising  out  of  the  Nature  of  the  Term 
itself. 

The  term  involves  in  itself  three  elements, —  mark  or 
property,  object,  name. 

1.  Considered  as  made  up  of  marks,  terms  are  divided, 
(1),  by  the  presence  or  absence  of  such  marks  into  positive 
and  non-positive;  (2),  by  the  separation  or  connection  of 
the  attributes  with  objects,  into  abstract  and  concrete. 

(1.)  All  terms  are  either  positive  or  non-positive.  A  positive  term 
is  one  that  implies  the  presence  of  some  real  mark  or  property,  as 
man,  tree,  good.  A  non-positive  term  is  one  that  implies  the  absence 
of  such  mark  or  property,  as  not-man,  uncertain,  deaf.  Non-positive 
terms  are  either  negative  or  privative.  A  negative  term  is  one  that 
implies  simply  the  absence  of  any  real  mark,  as  not-tree,  not-good, 
uncertain.  Terms  apparently  negative  are  often  positive  in  reality, 
as  immortal,  the  word  meaning  not  only  not  subject  to  death,  but 
living  for  ever.  So  terms  apparently  positive  are  often  negative, 
as  idle,  which  is  equivalent  to  not  working,  or  not  disposed  to  work. 
Privative  terms  are  equivalent  to  a  positive  and  negative  term  taken 
together.  They  mark  the  absence  of  certain  properties,  and  the  pres- 
ence of  others,  from  which  the  presence  also  of  the  former  might  nat- 
urally have  been  expected.  Such  terms  are,  blind,  unkind,  unholy. 
Blind  is  not  equivalent  to  not  seeing,  nor  to  not  capable  of  seeing,  but 
signifies  deprivation  of  sight  in  some  being  which  might  have  been 
expected  to  have  it. 

(2.)  All  terms  are  either  abstract  or  concrete.  Abstract  terms  are 
those  which  embody  abstracts  or  marks  or  properties  as  apart  from 
the  objects  to  which  they  properly  belong,  as  coldness,  hardness.  Of 
the  innumerable  abstracts  formed,  the  mind  suffers  the  greater  number 
to  pass  without  naming,  but  fixes  some  by  names.  Thus  in  observing 
some  individual  man,  the  abstracts,  life,  intelligence,  feeling,  self- 


THE   FORMATION    OF    CONCEPTIONS.         53 

activity,  etc.,  are  seized  upon  and  fixed  singly  by  names ;  or  several 
of  them  together,  under  one  name,  as  intelligence,  feeling,  etc.,  under 
rationality;  or  all  the  marks  together  under  humanity.  Concrete 
terms  present  the  marks  or  qualities  in  connection  with  the  objects  to 
which  they  belong,  or  (as  indicated  by  the  derivation  of  the  word 
from  the  Latin  con  and  cresco,  or  con  and  cerno}  with  which  they  are 
grown  together  or  seen  together,  as  the  adjective  terms,  cold,  hard,  and 
the  substance  terms  or  substantives,  ice,  iron,  man. 

2.  Considered  as  embodying  objects,  terms  are  divided, 
(1),  by  the  number  of  objects  embodied,  into  singular  and 
universal ;  (2),  by  the  connection  of  the  objects  with  their 
marks,  into  connotative  and  non-connotative. 

(1.)  All  terms  are  either  singular  or  universal.  Singular  terms  are 
those  in  which  our  percepts  or  simple  apprehensions  are  embodied,  or 
our  general  notions  as  connected  with  our  perceptions ;  as,  Shakespeare, 
the  Great  Eastern,  this  man.  They  begin  with  embodying  simple  no 
tions,  but  gradually  rise  toward  the  expression  of  thought  proper  or 
general  notions.  They  are  of  three  kinds  :  proper  names,  individual- 
ized common  names,  and  collective  names.  Proper  names  are  singular 
concrete  terms  which  denote  an  individual,  but  do  not  necessarily 
indicate  or  express  any  properties  of  that  individual;  as,  George 
Washington,  Alexander  Hamilton.  There  is,  however,  a  tendency  in 
the  progress  of  thought  to  connect  with  and  designate  by  the  proper 
term  the  peculiar  qualities  of  the  individual  denoted  by  it.  We  say 
of  a  man  he  is  a  Washington  or  a  Caesar — meaning  to  bring  out  his 
patriotism  and  equanimity  or  his  ambition  and  universal  genius.  An 
individualized  common  term  is  one  which  expresses  the  simple  notion 
of  an  object  as  it  is  presented  to  us  in  the  concrete  with  more  or  less 
of  its  properties;  as,  this  table,  this  man,  yonder  mountain.  It  is 
usually  formed  by  adding  some  individualizing  or  limiting  word  to  a 
common  or  general  term  ;  as,  this  table,  that  man,  an  organ,  my  hat. 
The  collective  term  is  also  properly  a  singular  made  up  of  many 
objects  brought  together  into  the  unity  of  a  mass,  rather  than  that  of 
a  class ;  as,  the  House  of  Commons,  the  army,  a  regiment,  a  forest. 

The  universal  term  is  that  in  which  the  general  notion,  embracing 
concept  proper  and  class,  is  embodied.  It  is  universal,  as  it  embraces 
all  the  objects  possessing  the  common  marks  or  properties  involved  in 
it  as  an  attribute  term.  It  is  common,  or  general,  since  it  is  applicable 
to  any  and  every  one  of  these  objects,  as  living,  or  man,  is  applicable 
5* 


54  PRACTICAL    LOGIC. 

to  every  individual  of  the  human  race.  It  differs  from  the  collective 
term,  which  embraces  a  number  of  things  joined  together  in  one  mass, 
as  regiment,  Congress,  since  the  collective  is  not  applicable  to  each  and 
every  object  under  it.  Every  being  embraced  under  the  general  term, 
man,  is  a  man  ;  but  not  every  soldier  embraced  under  the  collective 
term,  army,  is  an  army.  When  the  concept  proper,  or  complement  of 
ID  arks  or  properties  in  a  general  term,  is  made  prominent,  it  is  used  as 
a  concept,  or  attribute,  term;  when  the  class,  or  complement  of  objects 
embraced  in  it,  is  made  prominent,  it  is  considered  as  a  class  term.  In 
he  propositions,  Jesus  was  man  ;  Jesus  was  a  man, — the  meaning  of 
the  first  is,  that  Jesus  had  the  marks  or  properties  of  a  man ;  of  the 
second,  that  he  belonged  to  the  class,  man.  In  the  first  proposition 
man  is  a  concept  or  attribute  term ;  in  the  second,  a  class  term. 

(2.)  All  terms  are  either  connotative  or  non-connotative.  A  conno- 
tative term  is  one  which  denotes  an  object,  and  notes  along  with  it  a 
mark  or  property.  A  npn-connotative  term  is  one  which  signifies  an 
object  only  or  a  property  only.  All  proper  names  are  non-connota- 
tive, since  they  denote  objects,  but  connote  no  property ;  as,  Wash- 
ington, London.  All  abstracts  of  qualities,  as  whiteness,  length,  are 
non-connotative,  as  they  denote  only  properties  without  connoting 
any  objects.  All  adjectives,  as  white,  just,  and  all  concrete  general 
names,  as  bird,  fish,  are  connotative,  since  they  denote  objects  and 
connote  properties. 

3.  Considered  as  words,  terms  are  divided,  (1),  by  self- 
interpretation,  into  notative  and  non-notative  or  symbol- 
ical ;  and  (2),  by  the  number  of  words  constituting  the 
term,  into  simple  and  complex. 

(1.)  All  terms  are  either  notative  or  symbolical.  This  distinction 
has  already  been  defined  and  illustrated  under  the  Second  Rule  of 
Denomination. 

(2.)  All  terms  are  either  simple  or  complex.  A  simple  term  is  one 
which  consists  of  only  one  word.  But  some  words  cannot  be  used  as 
terms,  although  they  may  form  parts  of  terms.  Hence  arise  complex 
terms,  which  are  made  up  of  combinations  of  words.  With  reference 
to  their  being  used  as  terms,  words  are  either  categorematic  (from  a 
Greek  word,  to  assert  or  predicate),  i.  e.,  such  that  they  can  stand 
alone  as  complete  terms  in  propositions ;  or  syncategorematic  (from 
the  Greek,  to  assert  or  predicate  along  with),  i.  e.,  such  that  they  can 
only  form  parts  of  terms,  since  they  must  be  used  with  other  words  to 


THE   FORMATION    OF    CONCEPTIONS.         55 

make  up  complete  terms.  To  the  former  belong  the  noun,  adjective, 
and  certain  parts  of  the  verb.  There  are,  however,  those  who  con- 
tend that  in  the  last  analysis  only  nouns  can  form,  terms.  Such  sen- 
tences, as  "  Dictionaries  are  useful,"  must  be  completed  by  adding 
books  or  things;  thus,  "Dictionaries  are  useful  books"  Adverbs, 
prepositions,  conjunctions,  etc.,  are  syncategorematic.  We  speak  of 
"  the  conservation  of  energy,"  "  the  conflict  of  religion  and  science," 
thus  uniting  many  conceptions  in  one,  and  embodying  them  in  a 
phrase.  In  the  statement,  "This  is  a  faithful  saying,  and  worthy  of 
all  acceptation,  that  Christ  Jesus  came  into  the  world  to  save  sinners" 
the  part  italicized  is  a  term  expressed  in  a  sentence.  Complex  terms 
are  formed  by  combining  syncategorematic  with  categorematic  words. 
Any  of  the  objects  and  properties  included  under  the  Predicables  may 
thus  be  combined  in  complex  terms. 

II.  Kinds  of  Terms  arising  out  of  the  Relations  of  Terms. 

Terms  are  divided,  1,  by  their  relation  to  one  another, 
into  relative  and  non-relative  or  absolute ;  and,  2,  by  their 
relation  to  the  objects  of  which  they  are  predicated,  into 
compatible  and  incompatible. 

1.  All  terms  are  either  relative  or  non-relative.     A  relative  term  is 
one  which  implies  some  other  of  which  we  may  predicate  it  as  its  cor- 
relative, as  father,  son ;  ruler,  subject;  cause,  effect.     Non-relative  or 
absolute  terms  are  such  as  do  not  imply  any  such  relative  object  or 
correlative,  as  tree,  stone. 

2.  All  terms  are  either   compatible  or  incompatible.     Compatible 
terms  are  such  as  can  be  applied  to  the  same  object  at  the  same  time. 
Contrary  terms  are  the  most  opposed  that  can  be  conceived  as  appli- 
cable to  the  same  object  at  the  same  time,  as  wise  and  foolish,  good 
and  bad.     They  are  not  compatible,  however,  when  used  in  a  strict 
sense ;  since  anything  which  is  absolutely  good  cannot  be  in  any  sense 
bad.   Incompatible  terms  are  such  as  are  entirely  excluded  from  appli- 
cation to  the  same  object  in  the  same  sense  at  the  same  time.     All 
contradictory  terms  are  incompatible,  as  wise  and  not- wise,  black  and 
not-black. 

These  various  distinctions  of  terms,  embodying  impor- 
tant distinctions  in  thought,  are  to  be  met  with  more  or 
less  frequently  in  all  the  profounder  discussions  in  science, 
philosophy,  and  theology.  Most  of  them  will  be  found  to 


66  PRACTICAL    LOGIC. 

be  of  value  in  the  subsequent  portions  of  Logic.    They  may 
readily  be  presented  in  outline  form  by  the  student. 

Praxis. — Apply  all  the  foregoing  distinctions,  as  far  as  possible,  to 
the  following  words  :  1.  Government.  2.  Industry.  3.  Art.  4.  Agri- 
culture. 5.  Joy.  6.  Jupiter.  7.  This  earth.  8.  The  consolations  of 
philosophy.  9.  Intemperance.  10.  Foolish.  11.  Sobriety.  12.  Hope- 
fulness. 13.  Psychology.  14.  Virtue.  15.  Non-relative.  16.  Abso- 
lute. 17.  Immortal.  18.  Deaf.  19.  From.  20.  Life. 

Select,  from  the  page  preceding  the  praxis,  the  following  kinds  of 
terms  or  words:  1.  Negative.  2.  Privative.  3.  Simple.  4.  Complex. 
5.  Concrete.  6.  Abstract.  7.  Relative.  8.  Absolute.  9.  Singular. 
10.  Universal.  11.  Syncategorematic.  12.  Notative.  13.  Symbolical. 
14.  Connotative.  15.  Non-connotative.  16.  Abstract.  17.  Concrete. 
18.  Collective.  19.  Attribute.  20.  Class. 


CHAPTER    II. 

THE   UNFOLDING   OP   CONCEPTIONS. 

CONCEPTION,  in  its  three  essential  elements,  conception 
proper,  classification,  and  denomination,  has  been  found  to 
result  in  three  products : 

First,  the  Concept  Proper,  embracing  content  or  contained 
properties ; 

Second,  the  Class,  embracing  extent  or  included  individ- 
ual objects; 

Third,  the  Term,  embodying  both  concept  proper  and 
class,  and,  therefore,  to  be  regarded  either  as  an  attribute 
term  or  as  a  class  term. 

The  processes  of  unfolding  these  products,  or  of  ascertaining  accu- 
rately and  exhibiting  systematically  and  completely  what  is  con- 
tained in  them,  are  the  processes  at  the  foundation  of  all  right  and  full 
understanding  of  the  materials  of  which  discourse,  whether  spoken  or 
written,  is  made  up.  It  is  evident  at  once  that  a  man  who  does  not 
understand  what  is  involved  in  such  conceptions  as  cause,  force,  expe- 


THE   UNFOLDING    OF    CONCEPTIONS..       57 

rience,  persistence,  can  neither  think  nor  discourse  intelligently  con- 
cerning them,  and  can  neither  hear  nor  read  intelligently  anything 
that  others  may  say  or  write,  which  involves  these  conceptions. 

As  the  products  of  conception  are  three,  the  processes  of 
unfolding  are  three : 

First,  the  unfolding  of  the  content  of  the  concept  proper. 
This  has  been  named  Metaphysical  Analysis,  but  has  also 
been  called  Logical  Partition. 

Second,  the  unfolding  of  the  extent  of  the  class.  This  is 
known  as  Logical  Division. 

Third,  the  unfolding  of  the  term.  This  will  be  known 
as  Logical  Definition. 

Logical  Partition,  Division  and  Definition  will,  there- 
fore, furnish  the  subjects  of  the  three  Sections  embraced 
under  the  Unfolding  of  Conceptions. 

Section  I,— Logical  Partition, 

Logical  Partition  is  that  form  of  analysis  which  takes  a 
concept  proper,  as  a  complex  of  properties  or  attributes, 
and  unfolds  the  component  properties.  In  other  words, 
Logical  Partition  is  the  complete  and  orderly  statement  of 
the  parts  of  the  content  of  a  concept,  or  the  separation  of 
a  complex  attribute  into  its  component  attributes. 

The  thought-whole  analyzed  in  partition  is  the  concept 
proper  which  is  an  attribute  or  intensive  whole. 

The  mind  contemplates  the  objects  presented  to  it  under  three  kinds 
of  wholes : 

1st.  Mathematical  or  Quantitative  Wholes,  or  Wholes  of  strict  In- 
tuition. This  inckides  two  kinds : 

a.  The  Numerical,  based  on  Time. 

b.  The  Geometrical,  based  on  Space. 

2d.  Essential  orThysical  Wholes,  or  Wholes  of  Observation.  This 
includes  two  kinds : 

a.  The  Substance,  as  composed  of  substance  and  attributes. 

b.  The  Causal,  as  composed  of  cause  and  effects. 


58  PRACTICAL   LOGIC. 

3d.  Logical  Wholes,  or  Wholes  of  Discursion  or  Thought.  This 
includes  two  kinds : 

a.  The  Attribute  or  Intensive  Whole,  or  Whole  of  Content. 

b.  The  Class  or  Extensive  Whole,  or  Whole  of  Extent. 

A  mathematical  whole,  called  also  a  quantitative,  an  intuitive,  an 
integrate,  whole,  is,  according  to  Hamilton,  one  composed  of  integral, 
or,  more  properly,  integrant  parts.  It  is  a  whole  every  part  of  which 
lies  out  of  every  other  part,  while  all  the  parts  together  make  up  the 
integer  or  complete  whole.  Thus  in  the  integrate  spacial  whole  of  the 
human  body,  the  head,  body,  and  limbs,  its  integrant  parts,  are  not 
contained  in,  but  each  lies  out  of,  each  other.  When  the  parts  of  an 
integrate  spacial  whole  are  separate  and  accidentally  thrown  together, 
the  result  is  a  mass  whole,  as  a  gallon  of  water,  a  pile  of  wheat,  a 
block  of  wood.  When  the  parts  of  an  integrate  numerical  whole  are 
thus  separate  and  accidentally  thrown  together,  the  result  is  a  collect- 
ive whole,  as  an  army,  a  forest.  These  wholes  are  analyzed  by 
mechanical  or  physical  partition. 

An  essential  whole,  called  also  a  physical  whole  and  a  whole  of 
observation,  is  the  kind  of  whole  with  which  observation  brings  us  in 
contact.  It  consists  of  substance  and  properties  either  of  quality  or 
of  action.  The  parts  do  not  lie  out  of  each  other,  but  substance  and 
property  permeate  and  modify  each  other.  Thus  in  gold  the  material 
substance  is  inseparably  connected  and  blended  with  the  properties  of 
quality  and  action,  metallic  and  reflecting  the  yellow  rays  of  light. 
These  wholes  are  analyzed  by  the  process  of  mental  analysis  already 
described. 

A  logical  whole,  called  also  a  whole  of  thought,  is  the  product  of 
the  power  of  conception,  and  is,  therefore,  a  creation  of  thought.  As 
a  concept  proper  it  is  analyzed  by  logical  partition ;  as  a  class  whole, 
by  logical  division. 

Logical  analysis  by  partition  and  division,  therefore, 
deals  with  the  logical  whole  in  its  two  forms,  partition 
having  particularly  to  do  with  the  logical  whole  as  an 
attribute  whole.  The  aim  of  partition,  to  unfold  the  con- 
tent of  an  attribute  whole,  will,  in  connection  with  the 
nature  and  make-up  of  this  whole  as  already  learned  from 
the  formation  of  the  concept  proper,  suggest  the  forms  and 
rules  of  the  process. 


THE  UNFOLDING  OF  CONCEPTIONS.    59 

Topic  First.— The  Forms  of  Logical  Partition. 

The  purpose  of  the  thinker  in  partition  is  to  attain  to 
completeness  in  the  work  of  unfolding  the  marks  or  prop- 
erties of  the  concept.  Such  completeness  may  be  either 
relative  or  absolute.  This  gives  the  two  forms  of  partition. 

I.  Relatively  Complete  Partition. 

A  partition  is  relatively  complete  when  complete  from 
the  thinker's  point  of  view  or  for  his  special  purpose.  It 
is  obvious  that  it  is  not  always  the  aim  to  bring  out 
all  the  possible  properties  included  in  the  four  predicable 
classes.  Thus  the  chemist  may  desire  to  bring  out  the 
properties  of  gold  as  an  element  or  as  a  metal ;  the  banker, 
as  a  medium  of  exchange ;  the  encyclopaedist,  in  these 
and  all  other  aspects.  It  is  thus  manifest  that  any  one 
of  many  points  of  view  may  be  made  available,  the  choice 
being  always  governed  by  the  object  of  the  thinker. 

The  point  of  view  may  be  some  one  of  the  four  kinds  of  properties, 
and  the  aim  to  reach  the  component  parts  from  this  point  of  view. 
The  concept  man  may  be  parted  by  qualitative  properties  into  ration- 
ality and  animality ;  or  by  active  properties,  or  as  a  causal  agency, 
into  self-acting,  thinking,  feeling,  etc. ;  or  by  properties  of  condition, 
into  temporal,  terrestrial,  etc. ;  or  by  relative  properties,  into  depend- 
ent, responsible,  sinful,  etc. 

Or  the  point  of  view  may  be  a  single  aspect  of  some  one  of  the  four 
kinds  of  predicable  properties.  E.  g.,  taking  active  properties  as  the 
starting-point,  man  as  a  causal  agency  operates  in  many  different 
spheres,  and  may,  therefore,  have  the  properties  unfolded  with  ref- 
erence to  any  one  of  these  spheres.  The  thinker  may  be  a  physicist 
and  so  may  regard  man  materially,  as  counterpoising  more  or  less 
weight  and  excluding  other  objects  from  the  same  space.  He  may  be 
a  chemist  and  so  may  regard  man  chemically,  as  forming,  by  decom- 
position, nitrogen,  carbon,  and  other  chemical  elements.  He  may  be 
a  physiologist  and  so  may  regard  man  organically,  as  breathing, 
digesting,  etc.  He  may  be  a  political  economist  and  so  may  regard 
man  industrially,  as  farming,  manufacturing,  trading,  or  as  producing, 
transporting,  consuming,  etc.  He  may  be  a  psychologist  and  so  may 


60  PRACTICAL   LOGIC. 

regard  man  spiritually,  as  thinking,  feeling,  willing,  etc.  He  may  be 
a  theologian  and  so  may  regard  man  religiously,  as  recognizing,  long- 
ing after  and  worshipping  God,  etc. 

II.  Absolutely  Complete  Partition. 

A  partition  is  absolutely  complete  when  the  aim  is  to 
give  an  exhaustive  analysis  of  a  concept,  or  to  present  all 
the  kinds  of  properties. 

In  such  partition  the  various  characteristics  of  man,  as  given  from 
the  four  points  of  view,  would  all  be  embraced.  Or,  to  take  another 
example,  gold  may  be  parted  by  qualitative  properties,  as  material, 
solid,  elementary  substance,  etc. ;  by  active  properties,  as  reflecting  the 
yellow  rays  of  light,  conducting  heat  and  electricity,  counterpoising 
great  weight,  etc. ;  by  relative  attributes  (including  condition  and 
relation  proper),  as  being  mainly  confined  to  particular  regions  of  the 
earth,  being  of  great  value  as  a  precious  metal,  being  the  standard  of 
values  in  exchange,  etc. 

Topic  Second. — The  Rules  of  Logical  Partition. 

The  rules  for  logical  partition  are  determined  by  its  aim 
to  unfold  systematically,  from  some  definite  point  of  view, 
the  properties  or  attributes  contained  in  a  given  concept. 

Rule  1st. — The  thinker  in  partition  should  first  fix  upon 
a  single  complement  of  attributes,  should  then  determine 
upon  the  proper  point  of  view  for  the  purpose  he  has  in 
mind,  and  should  finally  adhere  to  this  point  of  view 
throughout  the  entire  partition. 

This  is  the  law  of  unity.  The  danger  of  violating  it  arises  from 
the  fact  that  language  uses  the  same  term  or  the  same  form  of  ex- 
pression for  very  different  concepts  or  bundles  of  properties.  Man, 
from  the  point  of  view  of  the  physiologist,  has  very  different  marks 
from  man  as  considered  in  social  science  or  in  psychology  or  theology. 
Physiology  considers  man  as  a  material,  organized,  living  being ; 
social  science,  as  a  member  of  society  and  having  certain  social  wants 
and  instincts ;  psychology,  as  a  spirit  embodied ;  theology,  as  a  crea- 
ture and  subject  of  God.  The  law  of  unity  requires  that  the  proper 
point  of  view  be  fixed  upon  and  prohibits  the  mixing  up  of  proper- 
ties belonging  to  man  from  these  various  points  of  view. 


THE  UNFOLDING    OF   CONCEPTIONS.         61 

Rule  2d. — A  partition  should  be  complete  from  its  point 
of  view,  or  inclusive  of  the  whole  complement  of  proper- 
ties divided. 

This  is  a  form  of  the  general  law  of  completeness  or  adequacy  or 

integrity.  So  far  as  a  partition  is  incomplete  it  omits  something  essen- 
tial to  the  conception,  and  thus  fails  to  give  that  distinct  view  which 
requires  that  all  the  parts  be  presented  in  their  proper  relation  to  each 
other.  Moreover,  incomplete  partitions  are  necessarily  partial  or  one- 
sided, and  will  inevitably  lead  to  positive  error.  If,  for  example,  in 
analyzing  faith  as  a  Christian  virtue,  we  recognize  only  the  marks, 
knowledge,  assent  or  intellectual  belief,  and  sentiment  or  response  of 
the  heart,  leaving  out  all  moral  disposition  or  purpose,  we  make  faith 
involuntary,  and  so  take  from  it  the  essential  element  of  all  virtue. 
Such  faith  ceases  to  be  a  virtue.  Mr.  Mill  falls  into  a  like  error  in 
analyzing  cause,  as  invariable  antecedence,  thereby  omitting  efficiency, 
the  principal  and  essential  property  involved  in  causation. 

Prof.  Day,  in  writing  of  the  general  Law  of  Adequacy  in  analysis, 
says:  "  The  practical  importance  of  a  careful  observance  of  this  Law 
of  Logical  Analysis  is  to  be  seen  in  the  fact  that  by  far  the  greatest 
part  of  erroneous  opinion  in  all  departments  of  knowledge  arises  from 
the  incomplete  apprehension  of  the  objects  of  knowledge.  Most  dis- 
sensions in  science  and  in  belief  would  be  ended  by  a  complete  survey 
of  all  the  constituent  elements  of  the  matter  in  dispute.  It  is  mainly 
because  the  parties  look,  one  at  one  element,  the  other  at  another,  and 
each  to  the  exclusion  from  his  view  of  some  element  or  character  im- 
portant to  a  correct  opinion,  that  any  dissension  arises."  This  holds 
with  special  force  in  partition,  since  this  process  deals  with  the  prop- 
erties, involved  in  the  essential  nature  and  make-up  of  things,  upon 
which  all  scientific  classification  depends. 

If,  for  example,  murder  is  analyzed  into  the  elements,  taking  of 
human  life,  deliberate  purpose,  then  the  act  of  the  sheriff  in  hanging 
a  murderer,  or  the  killing  of  another  in  self-defence,  would  be  murder. 
The  essential  element  of  malice  is  omitted  in  the  analysis.  Or,  again, 
if  virtue  is  analyzed  as  embracing  intelligence  and  conformity  to  the 
law  of  right,  omitting  intention,  then  the  act  of  every  hypocritical 
Pharisee  in  giving  alms  might  be  termed  virtuous.  On  the  other 
hand,  if  right  intention  is  embraced  in  the  partition,  and  conformity 
to  the  law  of  right  omitted,  the  acts  of  the  fanatic  and  enthusiast 
might  be  termed  virtuous.  It  is  only  by  taking  in  all  the  elements 
that  error  is  escaped.  Or,  once  more,  if  the  characters  of  the  rose  are 
6 


62  PRACTICAL    LOGIC. 

given,  as  a  shrub,  producing  flowers,  having  thorns,  the  rose  might  be 
confounded  with  any  thorn-bush.  All  such  possibilities  of  error  are 
eliminated  when  the  characters  are  fully  enumerated  as  they  are  in 
the  scientific  text-books  of  Botany. 

Rule  3d. — A  partition  should  be  exclusive,  i.  e.,  it  should 
shut  out  all  marks  or  characters  not  belonging  to  the  sub- 
ject. 

This  rule  corresponds  to  the  Law  of  Parcimony  under  observation. 
It  is  violated  if  education  is  made  to  embrace,  drawing  out  of  the 
powers,  putting  them  to  use  by  their  proper  exercise,  in  the  study  of 
the  physical  sciences,  in  a  scientific  school.  The  use,  the  kind  of  study, 
and  the  place  are  none  of  them  essential  to  the  process,  and  they  should, 
therefore,  be  excluded.  So  money  may  be  analyzed  into  the  charac- 
ters, stamped  metal,  means  of  exchange.  This,  however,  would  not 
apply  to  most  of  the  money  in  use  in  civilized  lands,  as  most  of  it  is 
not  metallic.  Money  embraces  the  characters,  representative  of  value, 
means  of  exchange,  passing  current,  so  that  metallic  is  not  an  essen 
tial  characteristic. 

Rule  4th. — A  partition  should  be  orderly  in  the  arrange- 
ment of  the  component  elements. 

This  requires  that  some  principle  of  arrangement  should 
be  seized  upon  and  made  use  of  in  the  statement  of  the 
elements  of  the  complex  thought  analyzed.  It  also  requires 
that  in  any  continued  process  of  partition  the  elements  ob- 
tained should  be  arranged  so  as  to  bring  out  the  relations 
of  co-ordination  and  subordination. 

In  analyzing  man,  in  its  intrinsic  elements,  by  partition,  we  may 
begin  with  the  visible  and  tangible  and  proceed  to  the  higher  invis- 
ible and  intangible.  The  resulting  partition  will  be,  animal  attributes 
or  animality  and  rational  attributes  or  rationality.  Analyzing  ani- 
mality,  we  may  again  proceed  from  lower  elements  to  higher.  The 
result  will  be,  attributes  of  matter  or  corporeity,  of  organization,  of 
life,  of  sentiency,  of  voluntary  motion.  On  the  same  principle  of  pro- 
cedure, rationality  will  yield  the  properties  of  intelligence,  emotion, 
and  endeavor.  The  rule  given  requires  such  orderly  procedure  and 
arrangement  in  the  work  of  partition.  In  the  partition  of  man.  it 


THE  UNFOLDING  OF  CONCEPTIONS.    63 

would  forbid  the  mingling  of  the  two  sets  of  attributes  and  the  co- 
ordination of  any  of  the  set  of  attributes  resulting  from  the  second 
step  in  the  partition,  as  sentiency,  with  animality  or  rationality. 

In  an  exhaustive  process  of  partition  each  of  these  elements  should 
be  still  further  divided  into  its  component  properties,  until  the  ulti- 
mate elements  are  reached.  For  example,  corporeity  would  give 
extension  in  length,  breadth  and  thickness,  weight,  etc.  Organization, 
life,  etc.,  would  each  be  found  to  yield  component  elements  co-ordinate 
with  those  of  corporeity. 

Praxis. — Give  exhaustive  Partitions  of  the  following  Concepts,  test- 
ing the  work  by  the  Rules:  1.  Money.  2.  Englishman.  3.  The  love 
of  God.  4.  Life.  5.  Salvation.  6.  Genius.  7.  Despair.  8.  Forgive- 
ness. 9.  Heaven.  10.  Duty.  11.  Manliness.  12.  Wisdom.  13.  Jus- 
tice. 14.  Beauty.  15.  Prophet.  16.  Foresight.  17.  Value.  18.  For- 
titude. 19.  Egotism.  20.  Selfishness.  21.  History.  22.  Philosophy. 
23.  Benevolence.  24.  Charity.  25.  Eternity.  26.  Omnipotence. 
27.  Politeness.  28.  Explanation.  29.  Confirmation.  30.  Design. 

Give  the  component  elements  of  the  following  Concepts,  stating  the 
kind  of  whole  and  the  point  of  view,  and  showing  that  the  Partition 
is  in  each  case  made  in  conformity  to  the  Rules  given :  1.  The  violet. 
2.  The  diamond.  3.  Botany.  4.  Habit.  5.  Hope.  6.  Affection. 
7.  Religion.  8.  Art.  9.  Fine  Arts.  10.  The  orange.  11.  Carbon. 
12.  Monsoon.  13.  Partition. 

Examine  the  following  Partitions,  stating  the  kind  of  whole  and 
the  point  of  view,  showing  whether  they  conform  to  the  Rules,  and, 
in  case  they  do  not,  correcting  or  completing  the  Partition  according 
to  the  Rules : 

1.  Government  =  Intelligent  power,  ordered   by  law,  controlling 
action. 

2.  Duelling  =  Fighting  of  two  persons,  mutual  agreement,  intent  to 
kill,  deadly  weapons. 

3.  Lie  =  Enunciation  of  what  is  false,  intent  to  deceive,  violation 
of  some  obligation  to  give  to  others  the  truth. 

4.  Novel  =  Fictitious  story,  central  interest  in  love,  artistic  con- 
struction. 

5.  Contract  —  Two  parties,  mutual  promise,  mutual  obligation. 

6.  Charity  —  Compassion  and  sympathy  for  the  needy,  kindly  and 
affectionate  provision  for  the  need,  wise  administering  of  the  relief. 

7.  Circle  =  A  curved  line,  drawn  round  a  given  point. 

8.  Planet  =  A  star  wandering  in  the  heavens. 


64  PRACTICAL   LOGIC. 

9.  Triangle  =  A  plane  figure,  three  sides,  three  angles  equal  to  two 
right  angles. 

10.  Parallelogram  =  A  plane  figure,  four-sided,  opposite  sides  equal 
and  parallel,  opposite  angles  equal. 

11.  Fluid  =  Material  substance,  yielding  easily  to  pressure,  parts 
readily  changing  relative  position  without  separation,  gaseous  form. 

12.  Whale  =  A  large  fish,  living  in  cold  regions,  useful,  yielding  oil. 

13.  Education  =  Instruction,  moral  discipline,  training. 

Section  II,— Logical  Division. 

Logical  Division  is  that  form  of  logical  analysis  which 
takes  a  conception  as  a  genus  or  class  whole  and  unfolds  its 
component  species.  In  the  words  of  Ueberweg  :  "  Division 
is  the  complete  and  orderly  statement  of  the  parts  of  the 
extent  of  a  notion,  or  the  separation  of  a  genus  into  its 
species." 

Note. — The  student  needs  to  distinguish  carefully  between  partition  and 
division.  The  former  takes  a  concept  proper  or  attribute  whole  and  separates 
it  into  its  component  properties ;  the  latter  takes  a  genus  or  class  whole  and 
separates  it  into  its  component  species  made  up  of  individuals. 

The  grounds  or  principles  of  division  are  found  in  the 
concept  proper,  or  the  common  properties  by  which  the 
objects  in  the  class  were  originally  classified.  These  prop- 
erties embodied  in  the  concept  proper,  and  making  up  its 
content,  have  been  called  the  base,  since  they  are  at  the 
foundation  of  both  concept  and  class.  The  possible  prin- 
ciples of  division  in  any  given  case  are,  therefore,  only 
limited  by  the  number  of  properties  and  combinations  of 
properties,  intrinsic  and  extrinsic,  contained  in  the  base 
and  unfolded  by  partition. 

Thus  the  class  man  has  a  content  or  base  of  two  complex  intrinsic 
properties,  animality  and  rationality.  The  class  may  he  divided  by. 
any  property  embraced  in  these.  It  may  be  analyzed  into  animal 
parts, — by  the  material  properties,  of  extension  in  length,  of  weight 
and  of  color,  giving  tall  and  short ;  heavy  and  light ;  white,  tawny, 
and  black :  by  the  properties  of  organization,  giving  sanguine,  nerv- 
ous, and  bilious;  etc.,  etc.  Or  man  may  be  divided  into  rational 


THE   UNFOLDING    OF    CONCEPTIONS.         65 

parts, — by  different  properties  of  intelligence,  giving  cultivated  and 
uncultivated ;  enlightened  and  barbarous ;  learned  and  unlearned ; 
imitative  and  creative ;  etc. :  by  the  comparative  prominence  of  the 
intelligence,  sensibility,  and  will,  giving  intellectual,  sentimental,  and 
practical.  Or  it  may  be  divided  by  both  animal  and  rational  parts 
combined, — by  language,  giving  Aryan,  Semitic,  and  Turanian ;  by 
race  constitution,  giving  Caucasian,  Mongolian,  etc. ;  and  the  like. 
Man  has  also  a  base  of  many  extrinsic  properties,  or  properties  of  con- 
dition and  relation,  which  may  also  furnish  innumerable  other  prin- 
ciples of  division.  It  may  thus  be  divided  by  relation  to  place,  as 
European,  Asiatic,  etc. ;  islanders  and  dwellers  on  the  continents ; 
men  of  the  torrid,  temperate,  and  frigid  zones  ;  and  the  like :  by  rela- 
tion to  time,  into  ancient  and  modern ;  or  ancient,  mediaeval,  and 
modern  ;  antediluvian  and  postdiluvian  ;  old,  middle-aged,  and  young ; 
and  the  like :  or  by  relation  proper,  into  bond  and  free ;  rulers  and 
ruled ;  and  the  like. 

Topic  First. — The  Forms  of  Logical  Division. 

The  principal  forms  of  logical  division  are  the  artificial 
or  dichotomous  and  the  natural.  Either  of  these  may  be 
single  and  unextended  or  complex  and  extended. 

1.  The  simplest  form  of  division  is  the  artificial  or  di- 
chotomous, or  that  which  arrives  at  two  members  which  are 
contradictories. 

For  example :  animals  are  rational  and  irrational,  or  vertebrate  and 
invertebrate;  angles  are  right  and  not-right  or  oblique;  oblique 
angles  are  acute  and  not-acute  or  obtuse ;  the  ancients  were  Jews 
and  Gentiles,  or  Greeks  and  barbarians,  or  bond  and  free. 

Such  division  is  said  by  the  logicians  to  be  strictly 
logical,  considering  merely  the  form  of  the  thought  and 
not  requiring  any  knowledge  of  what  the  concepts  mean 
in  order  to  assure  us  that  the  division  is  correct  and  ex- 
haustive. But,  as  Ueberweg  has  remarked,  "it  labors 
under  the  defect  that  the  species  classed  under  the  nega- 
tion are  left  indefinite.  Through  the  unimportance  of  the 
principle  of  division,  or  by  reason  of  the  number  of  species 
included  in  the  negative  and  contradictory  notion,  the 
division  may  become  worthless." 
6*  E 


66 


PRACTICAL    LOGIC. 


Substance. 


Thus,  the  division  of  the  universe  into  partridges  and  not-partridges 
is  of  no  value,  both  because  of  the  worthlessness  of  the  ground  of 
division  and  the  indefiniteness  of  the  negative  notion. 

The  process  of  dichotomous  division  may  be  extended 

until  the  lowest  species  or  individuals  are  reached.  There 
are  two  forms  of  this  extended  dichotomous  division,  a  loose 
form  and  a  strict  one. 

In  the  loose  form  the  principles  of  division  are  seized  upon  suc- 
cessively as  the  new  occasions  of  division  arise.  This  is  illustrated 
by  what  is  known,  from  its  author,  the  Greek  logician  Porphyrius,  as 

the  Tree  of  Porphyry,  which, 
starting  with  substance  as  the 
highest  genus,  closes  with  man 
as  the  lowest  species,  and  with 
Socrates,  Plato,  etc.,  as  the  indi- 
viduals. 

It  will  be  observed  that  the 
successive  principles  of  division 
are  the  qualities  implied  in  cor- 
poreal, animate,  sensible  (or  sen- 
tient), and  rational.  It  is  evident 
that  the  divisions  on  the  nega- 
tive side,  incorporeal,  insensate, 
etc.,  are  also  capable  of  like  sub- 
division with  those  on  the  posi- 
tive side. 

In  the  stricter  form  of  dichot- 
omous division,  one  principle  of 
division  is  carried  through  the 
entire  series  of  subdivisions.  In 
this  case  it  is  necessary  to  select 
at  the  outset  some  mark  or  attri- 
bute of  the  original  class,  as  the 
principle  on  which  the  successive 
divisions  shall  be  made.  This 


Corporeal. 


Animate. 


Sensible. 


Rational. 


Incorporeal. 


Inanimate. 


Insensible. 


Irrational. 


Socrates,  Plato,  and  others. 


may  be  illustrated  by  dividing  man  or  mankind  by  religion  as  the 
principle  of  division. 


THE    UNFOLDING    OF    CONCEPTIONS.         67 

Mankind 
I 


The  ists  Atheists 


Mon  otheists  Polytheists 

Chris 


tians  Non-Christians 


Pa  pists  Anti-Papists 


Jes  uits  Non-Jesuits 


Loyola  and  others 

In  this  example,  religion,  in  the  various  forms  in  which  it  appears 
among  mankind,  furnishes  successive  principles  of  division.  The  suc- 
cessive marks  or  characteristics  used  are,  a  personal  God,  the  one  God, 
God  in  Christ,  the  control  of  the  Pope,  Jesuitical  principles. 

2.  The  most  perfect  form  of  division  is  natural  division. 

"It  founds  itself,"  as  Ueberweg  has  said,  "on  the  essen- 
tial modifications  of  the  essentially  constitutive  (or  intrin- 
sic) attributes.  It  depends  on  the  essential  parts  of  the 
notion  or  class  to  be  divided.  It  is  called  natural  division 
in  the  same  sense  as  the  system  which  results  from  a  con- 
tinuous series  of  such  divisions  is  to  be  called  a  natural 
system." 

It  is  evident  that  divisions  of  this  kind  cannot  be  formed  in  any 
way  according  to  an  external  uniform  scheme.  It  is  incorrect  to  look 
for  an  equal  number  of  members  of  division  in  all  cases  in  divisions 
of  this  kind.  Thus  the  animal  kingdom,  divided  by  plan  of  structure, 
gives,  by  the  four  distinct  kinds  of  structure,  vertebrates,  articulates, 
molluscs,  and  radiates.  These  four  divisions  are  again  taken  up  and 
subdivided  in  the  Natural  System  of  Zoology.  Confining  the  natural 
subdivision  to  the  vertebrates,  we  find  at  least  five  subdivisions  recog- 
nized by  zoologists, — mammals,  birds,  reptiles  proper,  amphibians,  and 
fishes.  Again,  human  duties,  divided  by  the  object  toward  which  they 
are  directed,  naturally  fall  into  the  divisions,  individual,  social,  and 
theistic.  The  student  may  also  turn  to  the  classification  of  the  cupule- 
bearing  trees,  as  already  given,  for  another  illustration  of  natural 
division.  The  natural  divisions  are  seldom  dichotomous. 


68  PRACTICAL    LOGIC. 

3.  From  both  dichotomous  and  natural  division  often  arise 
the  trichotomy  or  threefold  division,  and  the  polytomy  or 
manifold  division. 

From  the  examples  already  presented,  it  is  manifest  that  natural 
division  is  often  found  to  be  trichotomous  or  polytomous.  It  is  like- 
wise true  that  these  forms  may  arise  from  a  condensed  statement  of 
extended  dichotomous  division.  Angles  are  divided,  by  the  degrees 
of  difference  in  the  direction  of  the  sides,  into  acute,  right,  and  obtuse. 
This  is  a  trichotomy  condensed  from  an  extended  dichotomy,  as  fol- 
lows :  angles  are  right  and  not-right ;  angles  not-right  are  acute  and 
obtuse.  The  trichotomy  is  drawn  from  this.  Mankind  are  Christians, 
Jews,  Mohammedans,  polytheists,  and  atheists,  is  a  polytomy  con- 
densed from  an  extended  dichotomous  process,  as  follows: 

Mankind 
I 


The  ists  Atheists 


Mon  otheists  Polytheists 


Christians  Non-Christians 


Jews  and  Mohammedans 

The  trichotomy  often  arises  because  the  parts  of  the  class  divided 
are  not  sharply  marked  off  or  separated  from  each  other.  Thus,  men 
divided  by  color  are  white,  tawny,  and  black.  The  present  condition 
of  a  sentient  being  may  be  one  of  pleasure,  of  indifference,  or  of  pain. 
Men  divided  by  age  are  young,  middle-aged,  and  old.  Action  con- 
sidered morally  is  good,  indifferent,  or  bad. 

Topic  Second. — The  Rules  of  Logical  Division. 

The  rules  for  division  naturally  arise  out  of  its  nature 
and  aim.  They  spring  either  from  the  principle  of  division, 
from  the  various  relations  of  the  parts  or  species  to  the 
whole  or  class  divided,  or  from  the  relations  of  the  divisions 
and  subdivisions  to  each  other. 

Rule  1st. — In  a  logical  division  the  first  requirement  is 
to  fix  upon  the  one  principle  of  division  suited  to  the  pur- 
pose in  view,  and  the  next  to  adhere  to  it  throughout. 


THE    UNFOLDING    OF    CONCEPTIONS.         69 

Several  particulars  need  to  be  noted  and  emphasized  in 
connection  with  this  rule. 

1.  There  must  be  some  principle  of  division  in  every 
case  as  the  reason  or  ground  for  the  division.     This  is  self- 
evident,  for,  as  Hamilton  has  said,  "  otherwise  there  would 
be  no  division  determined,  no  division  carried  into  effect." 

2.  The  principle  of  division  is  always  to  be  sought  in 
some  common  mark  or  property,  intrinsic  or  extrinsic,  of 
the  class  to  be  divided,  and  should  be  clearly  and  defi- 
nitely grasped. 

In  general,  it  is  manifest  that  the  essential  or  intrinsic  properties 
(those  of  quality  and  action)  have  most  to  do  with  determining  the 
character  pf  the  class  and  its  species.  These  properties  must,  there- 
fore, furnish  the  most  important  principles,  or  those  of  natural  division. 
In  dividing  man,  rationality  and  animality  furnish  more  character- 
istic divisions  than  the  extrinsic  properties  (those  of  relation). 

The  particular  end  which  the  thinker  has  in  view  must,  however, 
regulate  the  choice  of  the  principle  of  division,  so  that  in  certain  cir- 
cumstances that  principle  is  found  in  extrinsic  or  relative  properties. 
Man  is  divided  by  intrinsic  properties,  mental  and  physical  constitu- 
tion, into  Caucasian,  Mongolian,  etc.  Geographically,  man  may  need 
to  be  divided,  by  the  relative  property,  place  of  abode,  into  European, 
Asiatic,  etc. 

In  all  cases  the  principle  of  division,  whether  intrinsic  or  extrinsic, 
should  be  clearly  and  definitely  grasped.  Failure  in  this  inevitably 
leads  to  incoherent,  uncertain,  and  unsatisfactory  results.  Thus  when 
sentences  are  divided  into  indicative,  interrogative,  imperative,  and 
exclamatory,  no  principle  of  division  is  apparent ;  we  are  left  uncer- 
tain whether  these  are  all  the  kinds  of  sentences  and  whether  they 
should  all  enter  into  a  proper  division. 

3.  Every  division  should  have  only  one  principle. 

The  result  of  not  complying  with  this  requirement  is  what  is  called 
cross-division.  This  fault  brings  confusion  and  perplexity.  The 
division  of  governments  into  monarchical,  republican,  despotic,  aristo- 
cratic, and  hereditary,  violates  this  principle.  The  first,  second,  and 
fourth  of  these  divisions  have  as  their  ground,  the  persons  by  whom 
the  authority  is  exercised ;  the  third  has  its  ground  in  the  extent  of 


70  PRACTICAL    LOGIC. 

the  control ;  the  fifth  in  the  tenure  of  office.  Monarchy  and  aristoc- 
racy may  be  despotic  or  hereditary,  or  b  }th  or  neither.  In  short,  the 
divisions  cross  each  other  in  various  ways  and  the  whole  is  hopelessly 
confused.  The  same  thing  is  illustrated  by  the  division  of  books  into 
poetry,  history,  Latin,  French,  German,  morocco,  and  cloth.  Three 
principles  of  division  are  made  use  of:  the  subject-matter,  the  lan- 
guage in  which  written,  and  the  kind  of  binding.  This  results  in 
many  and  perplexing  cross-divisions. 

4.  The  principle   of  division  should  always  be  one  of 
some  importance  and  value. 

This  excludes  all  useless  and  foolish  divisions,  but  especially  the 
counterfeit  of  dichotomy  known  as  division  by  infinitation.  To  divide 
the  universe  of  being  into  man  and  not-man;  or  the  animal  kingdom 
into  parrots  and  not- parrots,  may  have  a  show  of  logic,  but. the  result, 
as  already  seen,  is  absolutely  worthless. 

5.  The  principle  of  division  should  always  be  suited  to 
the  purpose.      Very  different  divisions  of  the  same  class 
may  be  required  for  different  ends. 

For  the  purposes  of  Philology,  a  division  of  conjunctions,  by  the 
words  from  which  they  are  derived,  into  verbal,  adjective,  substantive, 
phrase  or  prepositional,  and  composite,  might  possibly  be  of  some 
service ;  but  as  a  division  for  the  purposes  of  grammar  (which  gives 
attention  to  the  thought  embodied  rather  than  the  origin  of  words)  it 
has  no  relevancy  and  is  of  no  value.  For  the  purposes  of  Grammar, 
the  principle  of  division  should  be,  by  the  relations  of  the  sentences  or 
parts  of  sentences  to  each  other,  into  co-ordinate  and  subordinate. 
These  again  should  be  subdivided,  by  the  special  forms  of  co-ordination 
and  subordination,  into  copulative,  adversative,  etc.,  final,  conditional, 
etc.  For  the  purposes  of  Philology  it  would  be  as  absurd  to  divide 
man  into  producers,  transporters,  and  consumers,  as  it  would  to  divide 
man,  for  the  purposes  of  Political  Economy,  into  Aryan,  Semitic,  and 
Turanian. 

Rule  2d. — A  division  should  be  complete  or  inclusive  of 
all  the  species  of  the  class  divided. 

These  species  into  which  a  class  is  divided  are  called 
the  members  of  the  division. 

If  these  species  or  members  of  the  division  taken  to- 


THE    UNFOLDING    OF    CONCEPTIONS.         71 

gether  do  not  exactly  equal  the  class,  then  the  division  is 
evidently  only  partial  and  imperfect.  This  rule  may  be 
transgressed  in  various  ways,  as  has  been  shown  by  writers 
on  logic. 

1.  The  rule  is  transgressed  when  members  of  a  division  are  left  out. 
For  example,  when  we  divide  the  actions  of  men  into  good  and  bad. 
To  this  we  should  add,  indifferent. 

2.  The  rule  is  transgressed  when  a  subdivision  is  co-ordinated  with 
a  division,  as  when  we  divide  mathematical  figures  into  solids  and 
plane  surfaces.     It  should  be  solids  or  surfaces,  since  this  is  the  funda* 
mental  division  (by  the  number  of  dimensions),  and  plane  and  curved 
surfaces  are  subdivisions  of  surfaces  by  another  principle. 

3.  We  violate  the  rule  when  we  bring  in  a  dividing  member  too 
much,  as  when  we  divide  mathematical  figures  into  solids,  surfaces, 
lines,  and  points.     Here  the  last  two  elements,  lines  and  points,  must 
be  excluded,  since  lines  and  points,  though  elements  of  mathematical 
figures,  are  not  themselves  figures. 

Rule  3d. — The  members  of  a  division  should  be  recipro- 
cally exclusive. 

This  requires  that  each  specific  part  brought  out  should 
be  entirely  different  from  every  other  such  part. 

1.  This  rule  is  violated  by  placing  a  subdivision  above  or  beside  a 
division  under  which  it  belongs,  as  when  human  actions  are  divided 
into  necessary,  free,  and  moral.      Free  actions  are  either  moral  or 
indifferent.     In  this  case,  therefore,  a  subdivision  of  free  actions, 
which  is  included  under  it,  is  placed  by  the  side  of  it.     Or,  again, 
when  the  sphere  of  Natural  History  is  divided  into  the  animal,  vege- 
table, and  mineral  kingdoms,  and  the  vertebrates ;  vertebrates  is  sub- 
ordinate to  animal,  and  as  a  subdivision  of  it  should  be  excluded  from 
enumeration  with  it. 

2.  The  rule  is  also  violated  when  more  principles  of  division  than 
one  are  used.   For  example,  when  we  divide  human  actions  into  neces- 
sary, free,  useful,  and  detrimental,  two  principles  of  division  are  used, 
necessity  and  utility,  and  the  result  is  that  the  enumeration  covers  the 
whole  class  of  human  actions  twice. 

Rule  4th. — A  division  should  proceed  immediately  from 
proximate  genera  to  proximate  species. 


72  PRACTICAL   LOGIC. 

Divisions  should,  as  far  as  possible,  be  continuous,  that  is,  the  notion 
must  first  be  divided  into  its  proximate,  and  then  into  its  remoter 
parts,  and  this  without  overleaping  any  one  part ;  or,  in  other  words, 
each  part  must  be  immediately  subordinated  to  its  own  whole.  It  is, 
therefore,  improper  to  divide  animals  into  elephants,  birds,  fishes,  etc. 
According  to  Cuvier,  as  modified  by  Agassiz,  the  system  of  Zoology 
which  gives  the  true  division  of  animal  is  as  follows : 

Kingdom Animal. 

Branch Vertebrates,  Articulates,  Mollusfo,  and  Radiates. 

Class Mammals,  Birds,  Reptiles,  Fishes,  etc. 

Elephants  belong  under  mammals.  In  the  division  given,  the  inter- 
mediate classes,  vertebrates  and  mammals,  are  overleaped. 

Such  an  overleaping  is,  however,  sometimes  allowed  for  the  sake  of 
brevity ;  but  this  only  when  the  omitted  members  can  be  readily  sup- 
plied in  thought.  This  is  illustrated  by  the  common  mathematical 
division,  already  given,  of  triangles,  into  right,  acute,  or  obtuse. 

Rule  5th. — A  division  should  be  orderly  in  the  arrange- 
ment of  the  specific  parts  into  which  the  class  is  divided, — 
i.  e.,  the  parts  should  be  placed  in  proper  co-ordination  and 
subordination. 

This  is  simply  the  requirement  that  in  the  statement  of  a  system  of 
division  everything  should  be  put  in  its  own  place.  The  rule  may  be 
illustrated  by  the  Intellect  or  Power  of  Cognition,  beginning  with  the 
Simple  Cognitive  Faculty. 

COGNITIVE  POWER  OR  INTELLECT  (divided  by  progressive  stages  of 
knowing) : — 

1.  Simple  Cognitive  Faculty  (by  kind  of  knowledges  acquired), — 

(1.)  Internal  Perception  or  Self-Consciousness,  giving  knowledge 

of  self; 
(2.)  External  Perception  or  Sense,  giving  knowledge  of  external 

world ; 
(3.)  Intuitive  Perception  or  Intuition  Proper,  giving  knowledge 

of  first  truths. 

2.  Conservative  Faculty  or  Memory  (by  psychological   elements  in 

keeping  knowledges), — 


THE    UNFOLDING    OF    CONCEPTIONS.         73 

(1.)  Retention,  keeping  knowledges,  out  of  consciousness; 

(2.)  Reproduction  or  Association  of  Ideas,  bringing  back  knowl- 
edges by  linking  them  together  ; 

(3.)  Representation  or  Imagination,  vividly  imaging  the  knowl- 
edges reproduced ; 

(4.)  Recognition,  connecting  the  present  imago  with  the  past 
knowledge. 

3.  Comparative  Faculty  or  Thought  (by  material  compared), — 

(1.)   Conception    or   Comparison   of    Objects,     forming    concepts, 

classes,  and  terms  ; 
(2.)  Judgment  or  Comparison  of  Concepts,   forming  judgments 

and  propositions ; 
(3.)  Reasoning  or  Comparison  of  Judgments,  forming  arguments 

and  conclusions. 

4.  Constructive  or  System-making  Faculty  (by  law  followed), — 

(1.)  Scientific  Construction  or  Construction  by  the  True,  giving 

scientific  system ; 
(2.)  Artistic  Construction  or  Construction  by  the  Beautiful,  giving 

aesthetic  system ; 
(3.)  Practical  Construction  or  Construction  by  the  Good,  giving 

practical  system. 

It  will  be  observed  that  neither  of  the  four  main  divisions  can 
change  place  with  any  other.  Simple  cognition,  or  the  power  of 
acquiring  our  simple  and  fundamental  knowledges,  must  act  before 
there  can  be  anything  for  memory  to  conserve;  conservation  or 
memory  must  act  before  comparison  can  have  any  material  to  elab- 
orate ;  comparison  must  do  its  work  in  order  to  furnish  the  materials 
for  construction.  The  powers  subordinate  to  these  four  must  likewise 
take  their  proper  places  of  subordination. 

Praxis. — Give  Divisions  of  the  following  Classes,  stating  clearly  the 
Principles  of  Division  and  whether  Artificial  or  Natural,  and  testing 
the  work  by  the  Rules :  1.  The  Races  of  Men.  2.  The  Nations  of  the 
Earth.  3.  Languages.  4.  Fruits.  5.  Heavenly  Bodies.  6.  Commerce. 
7.  Art.  8.  Industries.  9.  Governments.  10.  Churches.  11.  Emotions. 
12.  Desires.  13.  Ships.  14.  Triangles.  15.  Quadrilaterals.  16.  Laws. 
17.  Life.  18.  Dogs.  19.  Metals.  20.  The  Carnivora.  21.  Plants. 
22.  Roses.  23.  Stars.  24.  Processes  of  Rhetorical  Invention.  25.  Phys- 
ical Forces.  26.  Colors.  27.  Divisions  of  time.  28.  Flowering  Shruba 
7 


74  PRACTICAL   LOGIC. 

29.  The  ruminants.  30.  Insects.  31.  Forms  of  religion.  32.  Civiliza- 
tions. 33.  Laws.  34.  Societies.  35.  Educational  institutions.  36.  Me- 
chanic arts.  37.  Wars.  38.  International  alliances.  39.  Homicides. 
40.  Social  conditions.  41.  Human  relationships.  42.  The  rocks. 
43.  Occupations.  44.  Systems  of  unbelief.  45.  Monotheistic  systems. 
46.  Periods  of  human  history.  47.  Theistic  systems.  48.  Diversities 
of  genius.  49.  Poets.  50.  Phases  of  religious  character.  51.  Tem- 
peraments. 52.  Influences  in  formation  of  character.  53.  Influences 
of  the  Crusades  upon  European  civilization.  54.  Aims  in  life.  55.  Mo- 
tives influencing  human  conduct.  56.  Benefits  of  international  com- 
merce. 

Give  extended  and  complete  Divisions,  Dichotomous  or  Natural,  of 
the  following  Classes,  stating  the  Principle  and  testing  by  the  Rules : 
1.  The  vegetable  kingdom.  2.  Furniture.  3.  Birds.  4.  Cereals. 
5.  Fishes.  6.  Creeds  of  Christendom.  7.  The  Sciences.  8.  Foods  for 
man.  9.  Views  of  the  origin  of  the  universe.  10.  Forces  of  civili- 
zation. 

Examine  each  of  the  following  Divisions,  stating  the  Principle  of 
Division,  showing  whether  the  Division  is  Natural  or  Artificial  and 
whether  it  conforms  to  the  Rules ;  and,  in  case  it  does  not,  showing 
wherein  it  fails  and  correcting  and  completing  it: 

1.  Triangle  =  equilateral  and  equiangular. 

2.  Triangle  =  right-angled,  isosceles,  and  scalene. 

3.  Literature  =  history,  oratory,  and  poetry. 

4.  Literature  =  writings  historical,  religious,  poetical,  classical,  and 
current. 

5.  Government  =  democracy,  oligarchy,  aristocracy,  and  monarchy. 

6.  Government  =  absolute,  limited,  constitutional,  and  free. 

7.  Government  =  empires,  kingdoms,  dukedoms,  and  republics. 

8.  The  fine  arts  =  the  arts  of  free  beauty,  the  arts  of  dependent 
beauty,  and  the  arts  of  utility. 

9.  The  arts  of  free  beauty  =  music,  sculpture,  painting,  and  poetry. 

10.  The  arts  of  dependent  beauty  =  architecture,  landscape-garden- 
ing, embroidery,  and  decorative  painting. 

11.  Rectilinear  figures  =  triangles,  quadrangles,  rectangles,  paral- 
lelograms, and  polygons. 

12.  Sentence  =  simple,  compound,  and  complex. 

13.  Proposition  =  categorical,   hypothetical,   conditional,  and   dis- 
junctive. 

14.  Proposition  =  affirmative,  hypothetical,  and  negative. 


THE    UNFOLDING    OF   CONCEPTIONS.         75 

15.  Man  =  foot  and  horsemen. 

16.  Man  =  white,  black,  copper-colored,  olive-colored,  etc. 

17.  Thought  —  memory,  conception,  and  reasoning. 

18.  Poetry  =  didactic,  lyric,  and  epic. 

19.  Poetry  =  didactic,  lyric,  epic,  and  the  ballad  and  sonnet. 

20.  Matter  —  solid,  liquid,  aeriform,  and  radiant. 

21.  Duties  to  self  =  self-conservation,  self-culture,  and  self-conduct 
or  direction. 

22.  Carnivora  =  cats,  dogs,  civets,  weasels,  bears,  seals,  whales,  etc. 

23.  Mental  faculties  =  sense-perception,  memory,   conception,  ab- 
straction, judgment,  reasoning,  and  taste. 

Section  III,— Logical  Definition, 

Definition  in  general  is  the  mental  separation  of  an  object 
of  thought  embodied  in  language  from  every  other  object 
of  thought.  Logical  definition  is  the  accurate  unfolding  of 
the  signification  of  the  terms  which  embody  thought. 

The  various  forms  of  definition  and  the  indefiniteness  of 
view  on  the  whole  subject  of  definition  make  it  necessary 
to  consider  with  greater  care,  the  kinds  of  definition  and 
the  rules  of  logical  definition. 

Topic  First. — The  Kinds  of  Definition. 

The  word  definition  is  used  in  both  a  wide  and  loose  and 
in  a  narrow  and  strict  sense.  For  definition  in  the  former 
sense,  Hamilton  has  suggested  the  name  of  declaration, 
signifying  throwing  light  upon,  clearing  up.  It  may  also 
be  called  rhetorical  definition,  in  distinction  from  definition 
in  the  narrow  and  strict  sense,  which  is  called  logical 
definition. 

I.  Rhetorical  Definition. 

The  object  of  rhetorical  definition  or  declaration  is  to 
give  the  meaning  of  a 'word  loosely,  or  as  it  is  popularly 
understood  and  for  common  use,  rather  than  exactly  and 
for  scientific  ends.  It  does  not  necessarily  undertake  to 
unfold  essential  properties,  but  freely  uses  those  that  are 


76  PRACTICAL    LOGIC. 

accidental,  relative,  or  extrinsic.  It  is  called  description 
when  it  makes  use  of  a  number  of  concrete  characteristics, 
as  when  we  say  that  the  Caucasian  is  tall,  white,  graceful. 

1.  Various  popular  modes  of  defining  words  may  be  in- 
cluded under  rhetorical  definition.  These  should  be  dis- 
tinguished in  order  to  guard  against  certain  common  errors 
and  fallacies. 

(1.)  Etymological  definition  traces  the  root  of  a  word 
back  to  its  origin  and  defines  accordingly.  It  sometimes 
throws  much  light  upon  the  meaning  of  a  word  and  adds 
great  force  to  the  word. 

There  are,  as  has  been  shown  by  Trench  in  his  "Study  of  Words," 
most  important  lessons  of  history,  romance,  poetry,  and  morals  wrapped 
up  in  even  our  commonest  words.  In  bringing  out  this  meaning  by 
etymological  definition  it  is  necessary,  however,  to  guard  very  care- 
fully against  two  errors  in  particular, — that  of  fixing  upon  a  wrong 
etymology,  and  that  of  assuming  that  what  the  word  meant  at  the 
beginning  it  means  now.  Home  Tooke  furnished  an  illustration  of 
the  first  error  in  confounding  the  root  of  truth  with  that  of  trow, 
meaning  think,  and  then  concluding  that  "  truth  is  what  onetroweth," 
or  simply  a  matter  of  opinion.  A  better  philology  finds  for  truth  a 
root  which  would  make  it  signify  reality.  The  second  error  may  be 
illustrated  by  assuming  that  villain  is  still  simply  a  villager,  because 
that  was  the  original  meaning,  or  that  knave  is  still  merely  a  boy, 
because  that  is  what  the  word  once  meant. 

(2.)  Definition  by  word  analysis,  or  by  unfolding  the 
various  roots  of  which  a  word  is  made  up,  bringing  out 
and  combining  their  significations, — is  also  of  value  ;  but, 
since  it  involves,  in  most  cases,  a  knowledge  of  the  roots 
of  words,  it  is  liable  to  lead  to  the  same  errors  as  etymo- 
logical definition. 

For  example,  the  word  edify,  separated  into  its  two  component  parts, 
one  meaning  a  temple  and  the  other  to  make,  would  be  defined  etymo- 
logically  as  the  making  or  building  of  a  temple.  This  may  be  strikingly 
suggestive  of  the  greater  work  of  spiritual  building  signified  by  the 
word  as  now  used,  but  it  can  hardly  be  taken  in  the  literal  sense. 


THE    UNFOLDING    OF    CONCEPTIONS.         77 

Note.— The  subject  of  word  analysis  is  treated  of  in  such  works  as  Webb's 
"  Manual  of  Etymology,"  and  Swinton's  "  Word  Analysis."  The  student  of 
Logic  ought  to  be  familiar  with  it. 

2.  Rhetorical  Definition  may  also  proceed  by  the  vari- 
ous thought  wholes,  already  considered.  It  may  define 
words,  in  the  looser  way,  as  essential,  as  mathematical,  or 
as  logical  wholes,  by  giving  concrete  characteristics,  by 
using  synonymes,  or  by  casual  substitution  of  phrases. 

Such  careless  definition  sometimes  takes  the  form  of  mere  descrip- 
tion, or  the  naming  of  one  or  more  concrete  characteristics,  as  when 
we  say,  "  Man  is  a  risible  animal,"  "  Man  is  a  two-legged  animal 
without  feathers,"  "  The  east  is  where  the  sun  rises."  It  sometimes 
becomes  only  the  enumeration  of  synonymes,  as  in  much  of  the  defi- 
nition of  the  Dictionaries,  as,  "  Law  is  a  rule,  decree,  or  statute," 
"  Religion  is  piety."  It  sometimes  becomes  little  more  than  a  careless 
or  casual  substitution  of  phrases,  narrative  or  descriptive,  perhaps 
presenting  some  consequence  or  attendant  circumstance,  as  "  Wisdom 
leads  to  virtue  and  blessedness." 

Some  names  are  not  definable  except  by  rhetorical  definition.  It  is 
obvious  that  an  individual  cannot  be  logically  defined,  since  practi- 
cally we  cannot  form  a  notion  comprising  all  the  essential  marks 
which  it  has  in  common  with  any  other  notion  or  thing.  Description 
is  the  process  applicable  to  individuals.  On  the  other  hand,  simple 
notions,  or  those  containing  a  single  or  simple  mark,  cannot  be  logic- 
ally defined,  since  they  have  only  one  mark  and,  therefore,  no  differ- 
ential or  distinguishing  element.  Being,  for  example,  having  only 
one  mark,  existing,  cannot  be  unfolded,  as  there  is  no  complex  content 
to  unfold.  It  can  only  be  distinguished  from  nothing  or  non-entity, 
which  is  a  mere  negation,  or  defined  by  some  synonyme,  as  thing, 
existence. 

One  office  of  Logic  is  to  make  plain  the  insufficiency  of 
all  such  loose  forms  of  definition,  while  giving  command  of 
the  stricter  forms  of  logical  definition. 

II.  Logical  Definition. 

Logical  definition  separates  a  conception,  as  expressed  by 
a  word,  from  all  other  conceptions  by  fixing  upon  and  pre- 
senting the  essential  and  distinctive  property  or  properties. 
7* 


78  PRACTICAL   LOGIC. 

1.  Strict  or  perfect  logical  definition  has  two  forms. — 

The  general  term,  as  has  been  shown,  may  be  considered 
either  as  embodying  a  class  or  a  concept  proper,  in  other 
words,  either  as  a  class  term  or  as  a  concept  term.  Logical 
definition  should,  therefore,  regard  the  general  term  from 
both  these  points  of  view.  In  other  words,  it  is  of  two 
forms  :  one  defining  the  general  term  as  a  class  term  and 
the  other  as  a  concept  term  ;  the  former  dealing  with  extent 
or  contained  objects,  the  latter  with  content  or  contained 
properties. 

Note.— The  failure  to  recognize  this  twofold  form  has  led  to  various  differ- 
ences of  statement  concerning  the  nature  of  logical  definition.  The  old  logical 
definition  was  confined  to  the  conception  as  a  genus  or  class.  Professor  Davis 
proposes  to  confine  it  to  the  conception  as  a  concept  proper.  Logical  definition 
thus  becomes  substantially  synonymous  with  Partition  as  that  subject  has 
already  been  presented.  Other  logicians  confine  it  to  language  or  terms,  and 
make  it  apply  chiefly  to  class  terms.  The  view  here  taken  is  that  it  applies  to 
terms  as  embodying  both  classes  and  concepts.  It  is  thus  to  be  distinguished 
from  Logical  Division  and  Partition,  which  deal  with  thought  directly  rather 
than  indirectly  through  language. 

(1.)  Definition  of  the  Class  Term. — If  the  term  to  be 
defined  is  regarded  or  used  as  a  class  term,  the  definer  is 
required,  by  the  principles  of  logical  definition, — 

First,  to  name  the  next  higher  genus  to  which  the  class, 
considered  as  a  species,  belongs  ;  and, 

Secondly,  to  name  the  difference  (differentia),  or  specific 
difference  or  that  which  distinguishes  the  class,  considered 
as  a  species,  from  all  the  other  co-ordinate  species  under 
that  higher  genus. 

The  genus  and  difference  together  make  up  the  essence 
of  the  term,  because  they  embrace  the  essential  character- 
istics or  marks  of  the  class  embodied  in  the  term. 

Thus,  in  the  definition,  Man  is  a  rational  animal,  it  is  meant  that 
animal  is  the  next  higher  genus  to  which  man  belongs  as  a  species, 
and  that  rational  is  the  difference  or  that  which  distinguishes  man 
from  the  other  co-ordinate  species,  irrational  animal  or  brute. 

(2.)  Definition  of  the  Concept  Term. — If  the  term  to  be 


THE    UNFOLDING    OF    CONCEPTIONS.         79 

defined  is  regarded  or  used  as  an  attribute  or  concept 
term,  the  definer  is  required,  by  the  principles  of  logical 
definition, — 

First,  to  state  the  properties  of  the  higher  genus  to  which 
the  term,  considered  as  a  species,  belongs ;  and 

Secondly,  to  state  the  properties  which  distinguish  the 
term,  considered  as  a  species,  from  other  species  under  the 
higher  genus. 

Thus,  in  the  definition,  Man  is  rational  animal,  the  meaning  is  that 
the  concept  term,  man,  includes  animal  properties  or  animality,  and 
rational  properties  or  rationality.  The  properties  of  the  higher 
genus  are  included  under  animality,  and  those  of  the  species  under 
rationality. 

2.  Certain  imperfect  forms  of  logical  definition  are  also 
distinguished  by  logicians.     These  are  known  as  definition 
by  division,  by  colligation,  by  resolution,  and  by  compo- 
sition.     They  approach  the  strict  standard  of  definition 
more  nearly  than  does  rhetorical  definition.     They  are  in 
fact  statements  of  the  results  of  Division  and  Partition. 

The  first  two  forms  are  simply  different  statements  of  the  results  of 
Division  as  already  treated.  Definition  by  division  unfolds  a  class 
term  into  its  constituent  species  or  individuals,  as  when  we  state  that, 
"  The  animal  kingdom  consists  of  radiates,  mollusks,  articulates,  and 
vertebrates."  Definition  by  colligation,  which  is  the  reverse  of  defi- 
nition by  division,  gathers  up  and  unites  the  constituent  species  or  in- 
dividuals of  a  genus  or  species,  as  when  we  say  that,  "  The  Earth,  Mars, 
Mercury,  Venus,  Jupiter,  etc.,  are  the  planets."  The  second  two  forms 
are  simply  different  statements  of  the  results  of  Partition  as  already 
treated.  Resolution  brings  out  of  a  concept  term  its  component  prop- 
erties, as  when  we  say  that,  "  Man  is  rational  animal."  Composition, 
the  reverse  of  resolution,  gathers  up  and  unites  the  component  proper- 
ties, as  when  we  say  that,  "  Rational  animal  is  man." 

3.  By  an  extended  process  of  logical  definition  an  ulti- 
mate and  indefinable  term  is  reached.     In  making  such  a 
complete  explication  of  a  term  it  is  necessary  to  proceed  by 


80  PRACTICAL    LOGIC. 

defining  successively  the  genus  of  each  new  definition  until 
a  simple  notion  is  reached. 

Professor  Davis  has  illustrated  this  process  in  tabular  form  by  an 
extended  definition  of  carnivore. 

"  A  carnivore  is  a  flesh-eating  (=  differentia]  mammal  (=  genus). 
A  mammal  is  a  vertebrate  (=  g)  suckling  its  young  (=  d). 
A  vertebrate  is  an  animal  (=g)  having  an  internal  skeleton  (— d). 
An  animal  is  a  sentient  (=  d)  organism  (=  g). 
An  organism  is  a  living  (=  d)  being  (=  g)." 

The  process  comes  to  a  close  when  the  simple  notion,  being,  is 
reached.  The  result  of  the  definition  embraces  all  the  properties  con- 
noted by  the  concept  term,  carnivore,  and  all  that  would  be  brought 
out  by  a  Partition  of  that  term.  Stated  as  a  definition  by  resolution, 
it  becomes,  "Carnivore  includes  flesh-eating,  suck-giving,  internal- 
skeletoned,  sentient,  living,  existing." 

Ill,  Nominal,  Real,  and  Genetic  Definition. 

Logicians,  from  another  point  of  view,  distinguish  defi- 
nition as  nominal,  real,  or  genetic.  The  first  has  to  do  with 
the  mere  name  of  the  object  of  thought ;  the  second  with 
its  reality  or  essential  properties ;  the  third  with  the  cause 
which  generates  it. 

Nominal  or  verbal  definitions,  or  definitions  of  names  or  words, 
comprise  the  loose  forms  given  under  rhetorical  definition  or  declara- 
tion, as  when  we  say,  "  The  word  circle  signifies  a  uniformly  curved 
line."  A  real  definition  is  a  definition  of  the  thought  or  reality  em- 
bodied in  a  word.  It  unfolds  essential  marks,  and  is,  therefore,  strictly 
analytic.  It  comprises  the  forms  of  logical  definition  already  given. 
Thus  we  define  a  circle  as  "a  line  returning  upon  itself,  of  which  all 
the  parts  are  equidistant  from  a  given  point."  A  genetic  or  causal 
definition  is  one  which  states  the  rise  or  production  of  a  thing  as  the 
result  of  some  working  cause.  It  adds  something  to  what  is  contained 
in  the  defined  term,  and  hence  is  always  synthetic.  The  genetic  defi- 
nition of  a  circle  is,  "A  circle  is  formed  when  we  draw  around,  and 
always  at  the  same  distance  from,  a  fixed  point,  a  movable  point  which 
leaves  its  trace,  until  the  termination  of  the  movement  coincides  with 
the  commencement."  Only  such  notions  as  relate  to  quantities  repre- 


THE    UNFOLDING    OF   CONCEPTIONS.        81 

sented  in  space  and  time,  in  other  words  only  mathematical  notions, 
can  be  genetically  denned. 

Topic  Second. — The  Rules  of  Logical  Definition. 

The  rules  for  logical  definition  are  determined  by  its 
nature  and  aim.  They  spring  either  from  peculiarities  in 
the  origin  and  use  of  language,  or  from  the  nature  of  the 
thought  embodied  in  the  language. 

Rule  1st. — In  logical  definition  the  first  step  is  to  study 
carefully  the  term  to  be  defined. 

The  object  of  such  study  is  to  guard  against  the  common 
errors  in  defining,  which  arise  from  the  ambiguities  of  lan- 
guage. It  is  obvious,  therefore,  that  logical  definition 
requires  in  general  a  knowledge  of  language  and  the  prin- 
ciples of  interpretation.  In  particular  it  calls  for  a  knowl- 
edge of  the  kinds  and  sources  of  ambiguity  in  the  use  of 
terms. 

Professor  Jevons  has  presented  very  forcibly  the  importance  of  a 
thorough  acquaintance  with  the  great  imperfections  of  language.  He 
says,  "  Comparatively  few  terms  have  one  single  clear  meaning  and 
one  meaning  only,  and  whenever  two  or  more  meanings  are  uncon- 
sciously confused  together,  we  inevitably  commit  a  logical  fallacy.  If, 
for  instance,  a  person  should  argue  that  '  punishment  is  an  evil,'  and 
according  to  the  principles  of  morality  '  no  evil  is  to  be  allowed  even 
with  the  purpose  of  doing  good,'  we  might  not  at  the  first  moment  see 
how  to  avoid  the  conclusion  that  '  no  punishments  should  be  allowed,' 
because  they  are  evil.  A  little  reflection  will  show  that  the  word 
evil  is  here  used  in  two  totally  different  senses ;  in  the  first  case  it 
means  physical  evil  or  pain ;  in  the  second,  moral  evil ;  and  because 
moral  evil  is  never  to  be  committed,  it  does  not  follow  that  physical 
evils  are  never  to  be  inflicted,  for  they  are  often  the  very  means  of 
preventing  moral  evil." 

In  studying  the  subtle  variations  in  the  meaning  of  even 
our  common  words,  it  is  necessary  to  distinguish  between 
terms  as  univocal  and  equivocal.  Univocal  terms  are  those 
which  can  suggest  to  the  mind  no  more  than  a  single  mean- 

F 


82  PRACTICAL    LOGIC. 

ing.     Equivocal  terms  are  such  as  have  two  or  more  differ- 
ent meanings. 

1.  Strictly  univocal  terms  are  not  liable  to  mislead.     The  names  of 
individual  objects,  persons,  or  events  are  usually  fixed  and  certain  in 
their  meaning,  as  George  Washington,  Westminster  Abbey,  the  Atlan- 
tic Ocean.      The  instances  of  univocal  terms,  outside  of  individual 
names,  are  found  chiefly  in  technical  and  scientific  language.     Steam- 
engine,  railway   train,  oxygen,  hydrogen,   sulphuric   acid,  etc.,   are 
examples  of  what  may  be  found  in  connection  with  every  well-defined 
science.     It  will  be  seen,  however,  on  looking  more  closely,  that  gen- 
eral terms  are  not  strictly  univocal.     The  same  word  has  been  found 
to  embody  both  the  concept  proper  and  the  class.     Hence  the  first 
inquiry,  even  in  the  case  of  words  commonly  called  univocal,  should 
be,  7s  the  term  here  used  as  a  concept  term  or  as  a  class  term  f    The 
word  man  may  be  used  in  one  case  to  express  the  attributes  of  human- 
ity, and  in  another  to  express  the  species  or  individual  human  beings, 
and  clear  thinking  requires  that  the  thinker  should  know  precisely 
which  is  meant  in  any  given  case. 

2.  Equivocal  terms  are  exceedingly  numerous.      Equivocal  terms 
are  either  properly  ambiguous  or  homonymous. 

(1.)  A  properly  ambiguous  (from  Latin  ambigo,  to  wander,  hesitate, 
or  be  in  doubt)  term  is  one  that  has  come  to  be  used  in  different  sig- 
nifications. Equivocation  from  ambiguity  arises  in  two  different  ways : 

1st.  Through,  association,  i.  e.,  from  the  transfer  of  the  meaning  from 
the  thing  originally  denoted  by  the  word  to  some  other  thing  habit- 
ually and  intimately  associated  with  it.  The  word  church  originally 
denoted  the  building  in  which  religious  worshippers  assemble.  It 
has  come  to  mean  the  particular  body  of  worshippers  accustomed  to 
assemble  in  any  one  place ;  or  any  body  of  persons  holding  the  same 
opinions  and  connected  in  one  organization,  as  the  Church  of  Eng- 
land, the  Roman  Catholic  Church  ;  or  the  church  of  Christendom ;  or 
the  clergy  and  religious  authorities  of  any  sect  or  country.  The  word 
differs  entirely  in  meaning  as  used  by  a  member  of  the  Anglican, 
Greek,  Roman  Catholic,  Congregational,  Presbyterian,  or  any  other 
existing  church. 

2d.  Through  analogy,  i.  e.,  from  the  transfer  of  meaning  to  analo- 
gous objects.  We  speak  of  a  sweet  taste,  a  sweet  flower,  a  sweet 
tune,  a  sweet  face,  a  sweet  poem,  from  the  analogy  or  resemblance 
between  the  pleasure  given  by  the  flower,  tune,  etc.,  and  that  given 
by  something  sweet  to  the  taste,  as  a  lump  of  sugar. 


THE  UNFOLDING  OF  CONCEPTIONS.    83 

The  use  of  the  same  word  in  different  significations  renders  it  neces- 
sary in  many  cases  to  ask  the  question,  What  is  the  signification  in 
which  the  word  is  here  used?  When  the  philosopher  asserts  that 
"  experience  proves  the  eternity  of  matter,"  the  first  question  gives 
rise  to  such  as  follow :  Whose  experience  ?  The  philosopher's  ?  All 
men's?  All  men's  in  all  ages?  All  human  experience  plus  human 
speculation  ? 

There  are  some  ambiguous  words  which  should  be  carefully  studied 
in  order  that  an  intelligent  answer  may  be  given  to  the  question, 
Precisely  what  does  this  word  mean  in  the  present  instance  f  The  word 
all  is  an  example  of  such  ambiguity.  In  the  proposition,  "  All  these 
soldiers  are  individual  persons,"  all  is  used  distributively,  or  one  by 
one.  In  the  propositions,  "Not  all  men  are  soldiers,"  "All  men  are 
not  soldiers,"  all  with  the  negative  attached  is  not  equal  to  none,  but 
only  to  not  some,  so  that  the  all  in  this  case  is  only  equal  to  some. 

Words  often  change  their  meaning  in  the  course  of  time,  so  that  in 
studying  and  testing  the  works  of  past  thinkers,  there  is  need  to  ask 
the  question,  What  was  the  meaning  of  the  term  to  be  defined,  in  the 
day  when  this  author  wrote  f  When  the  authors  of  King  James's  ver- 
sion of  the  Bible  represent  the  Psalmist  as  praying,  "  Let  thy  tender 
mercies  speedily  prevent  us,"  careful  inquiry  should  be  made  into  the 
use  of  the  word  prevent,  about  the  opening  of  the  seventeenth  century. 
Such  inquiry  will  reveal  the  fact  that  the  word,  which  now  means  to 
go  before  one  to  hinder  him,  then  meant  to  go  before  to  anticipate  or 
supply  his  wants. 

(2.)  Homonyms  are  terms  which,  though  of  different  origins,  have 
accidentally  assumed  the  same  form  either  in  sound,  or  in  spelling,  or 
in  both.  Examples  of  the  first  kind  are  seen  in  such  words  as  right, 
wright,  write,  rite,  or  rein,  rain,  reign,  etc.  Examples  of  the  second 
kind  are  such  words  as  lead,  the  metal,  and  lead,  as  in  following  the 
guidance  of  another.  Examples  of  the  third  kind  are  such  words  as 
mass,  a  heap,  and  mass,  a  Roman  Catholic  religious  service.  An  im- 
portant instance  of  this  kind  of  equivocation  is  found  in  grammar,  "as 
between  the  numeral  one,  derived  from  an  Aryan  root,  through  the 
Latin  unus,  and  the  indeterminate  pronoun,  one  (as  in,  '  one  ought  to 
do  ones  duty'),  which  is  really  a  corrupt  form  of  the  French  word 
homme  or  man.  The  Germans  to  the  present  day  use  man  in  this 
sense,  as  in,  man  sagt,  i.e.,  one  says." 

Too  great  care  cannot  well  be  given  to  the  study  of  the 
terms  to  be  defined.  It  is  obvious,  from  the  examples 


84  PRACTICAL    LOO  1C. 

given,  that  any  failure  to  grasp  the  precise  signification  in 
which  a  single  important  word  is  used  may  utterly  vitiate 
a  whole  system  of  thought. 

Rule  2d. — A  logical  definition  should  bring  out  the  essence 
of  the  term  defined.  This  requires  scientific  accuracy. 

The  non-essential  or  accidental  properties  are  not  sufficiently  charac- 
teristic for  a  definition.  The  worthlessness  of  the  well-known  Platonic 
definition,  "  Man  is  a  two-legged  animal  without  feathers,"  as  contain- 
ing only  non-essential  marks,  was  easily  shown  by  Diogenes  when  he 
presented  a  plucked  chicken  as  Plato's  man. 

Since  general  terms  embrace  both  concept  and  class,  use 
is  to  be  made  of  both  Partition  and  Division  in  framing 
logical  definitions.  In  the  case  of  a  class  term  the  definition 
should  bring  out  the  next  higher  genus,  and  the  differentia, 
or  characteristic  of  the  term  defined  considered  as  a  species 
under  that  genus.  In  the  case  of  a  concept  term  the  defi- 
nition should  bring  out  the  properties  of  the  next  higher 
genus,  and  the  differentia,  or  characteristics  of  the  term 
considered  as  the  marks  of  a  species  under  that  genus. 

Definition  of  the  term  as  a  class  term  is  much  the  more  common 
form.  Such  definition  becomes  easy  when  the  student  has  once  learned 
to  put  the  term  defined  under  the  next  higher  class,  and  then  to  bring 
out  the  distinguishing  characteristics.  Rhetoric  is  defined  by  first 
putting  it  under  the  next  higher  class,  art,  or  practical  science,  and 
then  distinguishing  it  from  all  other  co-ordinate  species  of  art  by 
stating  its  object,  discourse, —  "Rhetoric  is  the  art  of  discourse." 
Patriotism  is  defined  by  first  putting  it  under  the  next  higher  class, 
love,  and  then  naming  the  special  object,  one's  country,  which  distin- 
guishes it  from  all  other  forms  of  love, — "  Patriotism  is  love  of  one's 
country." 

Rule  3d. — A  logical  definition  should  be  adequate  or 
precisely  equal  to  the  term  defined.  This  forbids  making 
the  definition  too  wide  or  too  narrow,  deficient  or  redundant. 

It  follows  that  a  good  definition  may  be  tested  by  simple  conver- 
sion, or  by  letting  the  subject  and  predicate  change  places.  If  the 
common  definition,  "Man  is  a  rational  animal,"  be  adequate,  then 


THE    UNFOLDING    OF    CONCEPTIONS.         85 

the  converse  will  be  true,  "  Every  rational  animal  is  man."  Strictly 
speaking,  we  are  not  absolutely  certain  of  the  truth  of  this  converse, 
for  although  it  may  be  true  of  this  earth,  there  may  be  in  other  worlds 
rational  animals  that  are  not  men.  The  definition  is,  therefore,  on 
this  supposition,  said  to  be  too  wide,  embracing  not  only  man,  but  all 
possible  rational  animals  in  other  worlds.  To  make  it  perfectly  ade- 
quate it  is  necessary  to  add  the  relative  property  expressed  by  terres- 
trial or  some  such  term,  as,  "  Man  is  a  rational  animal  of  this  earth." 
The  converse  will  then  be  strictly  true,  "  All  rational  animals  of  this 
earth  are  men."  On  the  other  hand,  if  man  be  defined  as  a  praying 
animal,  the  definition  is  said  to  be  too  narrow.  It  is  not  true  in  the 
strict  sense  that  no  animals  that  do  not  pray  are  men.  The  definition, 
in  other  words,  embraces  only  a  part  of  men.  Definitions  are  redun- 
dant when  they  add  to  the  essential  characteristics  derivative  or  unes- 
sential marks,  as,  "Man  is  a  rational  animal  that  laughs;"  they  are 
deficient  when  they  omit  some  essential  characteristic,  as,  "  Man  is  an 
animal."  To  the  latter  belong  definitions  by  co-ordinate  and  subordi- 
nate notions,  as,  "  An  odd  number  is  that  which  is  distinguished  from 
.  an  even  by  unity,"  "  Man  is  an  American." 

Ride  4th. — A  logical  definition  should  be  expressed  in 
language  as  perfect  as  possible. 

This  forbids  absurdity,  ambiguity,  verbosity,  tautology, 
and  obscurity  of  language,  as  well  as  circular,  negative,  and 
figurative  definitions. 

The  language  in  a  definition  should  be  clear  and  signifi- 
cant and  not  vague,  ambiguous,  or  senseless. 

When  Mr.  Spencer  defines  the  virtue  of  patriotism  as  national 
egoism,  his  definition  is  probably  accepted  by  the  mass  of  readers 
without  thought.  But  egoism  is  selfishness,  which  of  course  is  not  a 
virtue  at  all,  and  patriotism  is  not  a  national  but  an  individual  senti- 
ment. The  definition  is,  therefore,  absurd.  The  same  objection  holds 
against  Mr.  Spencer's  definition  of  evolution,  "  Evolution  is  a  change 
from  an  indefinite  incoherent  homogeneity  to  a  definite  coherent  hetero- 
geneity, through  continuous  differentiations  and  integrations."  The 
definition  is  pronounced  obscure  both  by  common  readers  and  by  those 
who  understand  the  strict  meaning  of  the  scientific  and  mathemati- 
cal phraseology.  A  British  critic  has  translated  the  definition  into 
English,  as  follows:  "  Evolution  is  a  change  from  a  nohowish  untalk- 
8 


86  PRACTICAL    LOGIC. 

aboutable-all-alikeness,  to  a  somehowish  and  in-general-talkaboutable- 
not-all-alikeness,  by  continuous  somethingelsifications  and  stickto- 
getherations." 

The  language  in  a  definition  should  be  precise  and  free 
from  surplus  words. 

Dr.  Johnson's  definition  of  oats,  "  Oats  is  a  grain  which  in  England 
is  generally  given  to  horses,  but  in  Scotland  supports  the  people''  vio- 
lates this  principle.  The  specific  difference,  expressed  by  the  words 
italicized,  is  entirely  unessential.  Dr.  James,  in  the  "  Anxious  In- 
quirer," says,  "  It  is  a  great  principle  that  subjective  religion,  or  in 
other  words,  religion  in  us,  is  produced  and  sustained  by  fixing  the 
mind  on  objective  religion,  or  the  facts  and  doctrines  of  the  word  of 
God."  Ruskin  says  of  this,  "  Put  entirely  out  the  words  I  have  put 
in  italics,  and  the  sentence  has  a  meaning,  but  by  its  verbosities  it  is 
extended  into  pure  nonsense;  for  'facts'  are  neither  ' objective '  nor 
'  subjective '  religion ;  they  are  not  religion  at  all.  The  belief  of  them, 
attended  with  certain  feelings,  is  religion ;  and  it  must  always  be 
religion  'in  us,'  for  in  whom  else  should  it  be  (unless  in  angels ;  which 
would  not  make  it  less  subjective)." 

The  language  in  definition  should  not  be  tautological, 
i.  e.,  a  definition  should  not  contain  the  name  of  the  thing 
defined,  nor  a  derivative,  synonymous,  or  correlative  term, 
for  this  would  be  to  define  a  thing  by  itself. 

This  is  violated  by  such  definitions  as  "  Life  is  the  vital  force."  It 
is  also  violated  by  what  is  called  the  circle  or  dialellon,  as,  "  A  board 
is  a  thin  plank,"  "  A  plank  is  a  thick  board."  John  Stuart  Mill's 
final  definition  of  cause  is  a  flagrant  violation  of  this  principle.  It  is 
as  follows :  "  We  may  define,  therefore,  the  cause  of  a  phenomenon  to 
be  the  antecedent,  or  concurrence  of  antecedents,  on  which  it  is  conse- 
quent invariably,  and  subject  only  to  the  absence  of  preventing  or 
counteracting  causes."  The  essential  idea  of  cause,  efficiency,  is  left 
out ;  the  last  and  perhaps  the  most  emphatic  word  in  the  definition  of 
cause  is  causes ;  and  the  affirmation  that  the  consequent  is  invariable 
is  followed  immediately  by  the  assertion  of  a  variable  condition. 

The  language  in  a  definition  should  be  perspicuous. 

The  aim  of  definition  is  to  place  the  thought  before  the  mind  with 
more  distinctness ;  hence,  terms  more  unintelligible  than  the  one  de- 


THE  UNFOLDING  OF  CONCEPTIONS.    87 

fined  should  be  avoided.  This  is  violated  by  Aristotle's  definition, 
"  The  soul  is  the  first  entelechy  or  energy  of  a  natural  organized  body 
possessing  life  potentially."  Definition  by  negative  marks  is  also  for- 
bidden by  this  principle,  where  definition  by  positive  marks  is  possible. 
To  define  man  as  not  a  brute  or  not  an  angel  gives  no  clear  concep- 
tion of  what  he  is.  Figures  of  speech  are  not  ordinarily  suitable  for 
definition,  e.g.,  "  Memory  is  the  warder  of  the  brain ;  "  "  The  Divine 
nature  is  a  circle  whose  centre  is  everywhere  and  the  circumference 
nowhere."  Such  definitions  make  thought  obscure  rather  than  distinct. 

Praxis. — Define  the  following  terms  Etymologically,  by  Analysis 
(where  possible),  Rhetorically  and  Logically,  stating  the  kind  of  Whole 
in  each  case  :  1.  Proposition.  2.  Development.  3.  Sincere.  4.  Lord. 
5.  Heathen.  6.  Tawdry.  7.  Saunter.  8.  Slave.  9.  Faculty.  10.  Op- 
eration. 11.  Education.  12.  Vulture.  13.  Instinct.  14.  Virtue. 
15.  Patriotism.  16.  Fanaticism.  17.  Ox.  18.  Gas.  19.  Ice.  20.  Oxy- 
gen. 21.  Diamond.  22.  Electricity.  23.  Sun.  24.  Moon.  25.  Load- 
stone. 26.  Gold.  27.  Sophomore.  28.  Voyage.  29.  Battle.  30.  War. 
31.  Sentence.  32.  Grammar.  33.  Rhetoric.  34.  Logic.  35.  Arith- 
metic. 36.  Straight  line.  37.  Circle.  38.  Point.  39.  Sphere.  40.  Vice. 
41.  Ghost.  42.  Spirit.  43.  Tribulation.  44.  Passion.  45.  Vexation. 
46.  Rage.  47.  Love.  48.  Desire.  49.  Expectation.  50.  Loafer. 

Note.— See  Trench  "  On  the  Study  of  Words" 

Define  the  words  from  number  36  to  number  39  inclusive,  nominally, 
really,  and  genetically. 

Examine  each  of  the  following  definitions,  stating  of  what  kind  it 
is,  showing  whether  it  conforms  to  the  Rules,  and,  in  case  it  does  not, 
showing  wherein  it  fails,  and  correcting  and  completing  it : 

1.  Grammar  is  the  science  of  language. 

2.  Philology  is  the  science  of  language. 

3.  A  triangle  is  a  rectilinear  figure  having  three  sides  and  three 
angles. 

4.  A  square  is  a  quadrilateral  having  all  the  angles  right  angles, 
all  the  sides  equal,  and  the  opposite  sides  parallel. 

5.  Malaria  is  that  which  induces  fever. 

6.  A  cone  is  a  solid  generated  by  the  revolution  of  an  angle  about 
one  of  its  sides. 

7.  Virtue  is  a  voluntary  act  done  in  obedience  to  the  law  of  God  for 
the  sake  of  everlasting  happiness. 

8.  Logic  is  the  art  of  reasoning. — WHATELY. 


88  PRACTICAL    LOGIC. 

9.  Logic  is  the  light-house  of  the  understanding. 

10.  Truth  is  the  agreement  of  a  cognition  with  its  object. — HAM- 
ILTON. 

11.  Truth  is  accordance  with  the  reality. 

12.  A  whale  is  a  large  fish  inhabiting  the  polar  seas,  and  furnishing 
oil  and  whalebone  as  articles  of  commerce. 

13.  Happiness  is  the  reflex  of  unimpeded  energy. — HAMILTON. 

14.  Life  is  that  condition  of  an  organized  being  in  which  it  is 
capable  of  performing  its  functions. — PORTER. 

15.  Life  is  definable  as  the  continued  adjustment  of  internal  rela- 
tions to  external  relations. — SPENCER. 

16.  Science  is  systematized  knowledge. 

17.  Mind  is  the  unextended. — BAIN. 

18.  Matter  is  the  permanent  possibility  of  sensation. — MILL. 

19.  Mind  is  a  conscious  string  of  sensations. 

20.  A  sphere  is  a  solid  generated  by  a  revolution  of  a  semicircle 
about  its  diameter  as  an  axis. 

21.  A  sphere  is  a  solid  or  volume  bounded  by  a  surface,  every  point 
of  which  is  equally  distant  from  a  point  within,  called  the  centre. — 
WORCESTER. 

22.  Education  is  the  training  of  the  intellectual  powers,  principally 
by  the  study  of  the  physical  sciences. 

23.  Knowledge  is  power. 

24.  Net-work  is  anything  reticulated  or  decussated  at  equal  dis- 
tances with  interstices  between  the  intersections. — DR.  JOHNSON. 

25.  A  saunterer  is  one  who  is  going  to  the  Holy  Land. 

26.  Law  is  a  lawful  command. 

27.  Gratitude  is  a  lively  sense  of  future  favors. 

28.  Gratitude  is  a  virtue  of  acknowledgment. 

29.  A  ruler  is  one  who  establishes  laws. 

30.  A  circle  is  a  curved  line  returning  upon  itself,  the  parts  of  which 
are  at  an  equal  distance  from  the  central  point. 

31.  Logic  is  the  electric  light  of  the  intellect,  the  cynosure  of  truth, 
the  physic  of  the  mind. 

32.  Man  is  an  animal  walking  on  two  feet. 

33.  Man  is  a  bimanous  mammal. 

34.  Monarchy  is  a  form  of  political  government  in  which  one  man 
is  sovereign. 

35.  Wealth  is  that  which  furthers  the  well-being  of  man. 

36.  The  soul  is  the  principle  by  which  we  live,  feel,  move,  perceive, 
and  understand. — ARISTOTLE. 


THE    UNFOLDING    OF    CONCEPTIONS.        89 

37.  Beauty  is  the  feeling  we  experience  in  recognizing  unity  amidst 
variety. 

38.  A  dragon  is  a  serpent  breathing  flame. 

39.  Fine  Art  is  the  embodiment  of  thought  in  sensuous  form. 

40.  Man  is  a  rational  being. 

41.  A  cat  is  a  domestic  animal. 

42.  A  dog  is  a  digitigrade  quadruped,  having  fixed  claws,  four  toes, 
and  a  recurved  tail. 

43.  Memory  is  that  power  of  the  human  soul  which  recalls  past 
knowledge. 

44.  Philosophy  is  the  science  of  principles. — UEBERWEG. 

45.  Philosophy  is  the  love  of  wisdom. 

46.  Dirt  is  matter  in  the  wrong  place. — LORD  PALMERSTON. 

47.  A  perception  is  an  impression  made  on  the  mind. 

48.  Mathematics  is  the  science  of  extension. 

49.  Snow  is  frozen  mist. 

50.  A  carnivore   is   flesh-eating,  suck-giving,    internal-skeletoned, 
sentient,  living,  existing. 

51.  A  seal  is  a  species  of  fish. 

52.  Honesty  is   a  species  of  policy  distinguished  from  other  co- 
ordinate species  by  being  the  best. 

53.  Dancing  is  a  refined  and  sublimated  modification  of  circum- 
ambulatory  locomotion. 

54.  Man  is  physically  a  living  machine. 

55.  A  conjunction  is  a  word  that  connects  words  and  sentences. 

56.  Matter  is  that  in  which  is  discerned  the  promise  and  potency  of 
all  terrestrial  life. — TYNDALL. 

57.  God  is  the  not-ourselves  which  makes  for  righteousness. — MAT- 
THEW ARNOLD. 

58.  Religion  is  cosmic  emotion. — CLIFFORD. 

59.  Evolution  or  development  is  essentially  a  combination  of  causes 
working  toward  a  particular  end. — McCosH. 

60.  The  conic  section  is  that  mathematical  figure  which  divides  into 
these  four  forms — circle,  ellipse,  parabola,  hyperbola. 

61.  The  sensibility  takes  that  to  be  good  which  warrants  or  prom- 
ises pleasure,  and  affects  us  pleasantly  ; — the  desires  rest  on  pleasant 
feelings. 

62.  The  feeling  of  the  pleasant  is  the  immediate  consciousness  of 
the  furtherance  of  life. — UEBERWEG. 

63.  Justice  is  a  square  number. 

64.  The  idea  of  the  good  is  the  sun  in  the  kingdom  of  ideas. — PLATO. 

8* 


90  PRACTICAL    LOGIC. 

65.  Nature  (Heaven  and  earth  and  all  that  is  therein)  is  the  body 
of  God. 

66.  The  state  is  man  writ  large. 

Define  the  principal  Terms  used  in  the  following  Sciences,  testing 
the  definitions  by  the  Rules:  1.  Arithmetic.  2.  Geometry.  3.  Botany. 
4.  Zoology.  5.  Grammar.  6.  Physical  Geography.  7.  Rhetoric.  8.  Psy- 
chology. 9.  Natural  Philosophy.  10.  Astronomy.  11.  Geology.  12.  Eth- 
ics. 13.  Political  Economy.  14.  Science  of  Government. 


SUMMARY   OF   RESULTS 

THE  aim  of  the  Logic  of  Conception  is  to  train  to  the 
best  thinking  and  fullest  appreciation  of  thought  in  the 
first  form.  The  degree  of  perfection  or  imperfection  with 
which  the  mind  grasps  its  conceptions  constitutes  what  is 
called  the  logical  quality  of  conception,  Our  grasp  of  con- 
ceptions is  perfect  in  proportion  as  it  is  clear,  distinct,  and 
adequate  :  imperfect  in  proportion  as  it  is  obscure,  confused, 
and  inadequate. 

A  conception  is  clear  when  it  is  simply  distinguishable  from  others ; 
obscure  when  it  is  not.  This  may  be  illustrated  by  experience  in 
gazing  upon  a  tree.  When  the  light  falls  upon  it  we  readily  distin- 
guish it  from  other  trees  and  objects  of  the  landscape,  and  the  view  is 
clear ;  but  when  the  mist  or  the  twilight  settles  around  it  we  can  no 
longer  distinguish  it  from  other  objects,  and  the  view  becomes  obscure. 
We  have  a  clear  conception  of  man  when  we  distinguish  it  from  inor- 
ganic matter,  plant,  animal,  etc. ;  so  long  as  we  are  unable  to  do  this 
our  conception  of  it  is  obscure. 

A  conception  is  distinct  when  we  not  only  distinguish  its  object 
from  all  others,  but  also  grasp  the  constituent  marks  or  parts  of  that 
object.  In  every-day  life  we  may  know  the  hand-writing  or  features 
of  a  person  from  those  of  all  others  and  yet  not  be  able  to  give  the 
characteristics  of  either.  This  is  true  in  conception, — we  may  be  able 
to  discriminate  man  from  mineral,  plant,  animal,  etc.,  and  yet  not  be 
able  to  give  the  characteristics  of  man.  Our  conception  is  confused  or 
indistinct.  Distinctness  requires  us  not  only  to  discriminate  between 


THE    UNFOLDING    OF    CONCEPTIONS.         91 

an  object  and  all  others,  but  also  to  know  the  distinctive  marks  or  parts 
of  that  object.  Our  conception  of  man  becomes  distinct  when  we  see 
that  it  includes  animality,  rationality,  and  terrestriality ;  until  then 
it  is  confused. 

A  conception  is  adequate  when  we  not  only  grasp  the  constituent 
marks,  but  also  the  marks  of  these  marks  ;  inadequate  when  we  fail 
to  do  this.  Perfect  adequacy  of  conception  is  reached  by  carrying  out 
the  complex  processes  of  Partition,  Division,  and  Definition  until  the 
lowest  component  attributes,  constituent  species,  and  characteristic 
marks  are  reached.  The  extent  to  which  these  processes  must  be  car- 
ried to  reach  a  practical  adequacy  of  conception  in  any  given  case  will 
depend  upon  the  exigencies  of  the  thinking  or  the  aims  of  the  thinker. 
The  conception  of  man  is  adequate  when  we  not  only  know  the  three 
marks  given  above,  but  have  also  gone  further  and  grasped  the  marks 
of  animality,  as  corporeity,  organization,  life,  sentiency,  voluntary 
motion ;  of  rationality,  as  intuition  of  first  truths  and  the  power  of 
thinking  and  acting  in  the  light  of  such  truths ;  of  terrestriality,  as 
limitation  to  the  earth  with  its  conditions  of  time  and  space. 

It  will  be  readily  seen  that  clearness  is  chiefly  attained 
through  Definition ;  distinctness  through  Partition  and 
Division  ;  adequacy  through  the  extended  processes  of  Par- 
tition, Division,  and  Definition. 

A  conception  is  true  when  it  corresponds  with  the  reality. 
The  aim  of  the  Practical  Logic  of  conception  is  fully  at- 
tained when  the  training  results  in  the  ability  of  the  thinker 
to  reach  true  conceptions  which  are  clear,  distinct,  and 
adequate. 


PART  II. 

THE  LOGIC  OF  JUDGMENT  OR  THE  PROPOSITION. 


THE  aim  of  the  Logic  of  Judgment  is  to  train  the  mind 
to  skill  in  dealing  with  the  second  Form  of  Thought. 

Definition.— (Judgment  is  that  form  of  thought  in  which 
we  compare  two  notions  and  mentally  affirm  their  union  or 
disunion,  on  the  ground  of  a  like  union  or  disunion  appre- 
hended in  the  objects  or  realities  which  the  notions  repre- 
sent The  result  of  the  operation  of  judging  is  a  complex 
form  of  thought  known  as  a  Judgment,  the  verbal  expres- 
sion of  which  is  called  an  Assertion  or  Proposition.  The 
connection  between  judgment  and  proposition  is  so  intimate 
that  the  two  terms  are  used  interchangeably. 

Note. — The  definitions  of  judgment  have  been  various.  Some  have  defined 
it  to  be,  the  affirmation  of  the  agreement  or  disagreement,  or  of  the  congruence 
or  confliction,  of  two  notions.  According  to  Thomson,  it  is  "  an  expression 
that  two  notions  can  or  cannot  be  reconciled— that  the  mark  of  the  one  may 
or  may  not  henceforward  be  assigned  to  the  other."  Manifestly  judgment  as 
thought  is  much  more  than  mere  affirmation,  whether  mental  or  verbal,  of  the 
agreement  or  disagreement  of  two  notions.  The  question  whether  the  form 
of  words,  "Man  is  intelligent,"  or,  "  Man  is  patent  elliptic,"  is  a  judgment  or 
embodies  a  judgment,  is  not  to  be  decided  by  affirmation  of  any  kind.  It  de- 
pends upon  the  knowledge  of  connection  existing  or  not  existing  between  the 
realities  or  objects  represented  by  the  words  and  notions. 

Ueberweg  comes  nearer  the  presentation  of  the  essence  of  judgment,  when 
he  makes  it  the  comparison  of  two  notions,  whose  forms  are  different  from 
but  belong  to  each  other,  and  the  mental  affirmation  of  their  union  or  disjunc- 
tion on  the  ground  of  like  relation  apprehended  between  the  objective  realities 

92 


THE   FORMATION   OF  JUDGMENTS.  93 

which  the  notions  represent.  The  all-important  thing  is  "  the  consciousness, 
whether  or  not  the  analogous  combination  exists  between  the  corresponding 
objective  elements.  As  the  individual  conception  corresponds  to  the  individ- 
ual existence,  so  the  judgment  in  its  various  forms  corresponds  to  and  is  the 
subjective  copy  of  the  various  objective  relations." 

The  desired  skill  in  judgment  can  only  be  acquired  by 
the  knowledge  and  use  of  the  principles  which  govern  the 
forming  and  unfolding  of  judgments.  The  subject  will, 
therefore,  be  considered  under  two  Chapters,  one  treating 
of  the  formation  of  judgments,  the  other  of  their  unfolding. 


CHAPTER   I. 

THE  FORMATION  OP  JUDGMENTS  OR 
PROPOSITIONS. 

THE  formation  of  judgments  is  manifestly  a  most  impor- 
tant work  of  thought.  Processes  of  reasoning  and  systems 
of  science  and  philosophy  are  made  up  of  combinations  of 
judgments,  and  if  the  judgments  are  not  properly  and 
thoroughly  established,  i.  e.,  if  they  are  not  true,  then  the 
arguments  and  systems  cannot  be  expected  to  prove  true. 
It  is,  therefore,  necessary  to  inquire  carefully  into  both  the 
process  and  products  of  judgment-forming. 

Section  I, —  The  Process  of  Judgment-Forming. 

The  definition  of  judgment  already  given  suggests  for 
consideration  the  following  Topics :  first,  ascertaining  and 
combining  the  elements  of  judgment;  second,  finding  the 
reasons  or  grounds  upon  which  the  truth  of  judgments  de- 
pends, or  the  verification  of  judgments. 

Topic  First. — The  Elements  of  Judgment. 

The  elements  of  judgment  are  ascertained  by  analyzing 
judgment  either  as  embodied  in  the  proposition  or  as  a 
form  of  thought.  From  the  former  point  of  view,  it  is 


94  PRACTICAL    LOGIC. 

made  up  of  two  terms  (so  called  because  they  are  the  ter- 
mini or  boundaries  of  the  proposition)  united  by  the  verb 
to  be  as  copula  (bond)  ;  from  the  latter  point  of  view,  it  is 
composed  of  two  notions  united  by  some  connecting  link  of 
thought. 

I.  The  Terms  or  Notions  in  Judgment. 

The  terms  or  notions  are  distinguished  as  the  Subject  or 
Subject  Notion,  or  that  about  which  the  assertion  is  made, 
and  the  Predicate  or  Predicate  Notion,  or  that  whose  union 
or  non-union  with  the  subject  is  affirmed.  In  logical  form- 
ulas the  subject  is  usually  expressed  by  S  and  the  predicate 
byP, 

The  various  notions,  already  considered,  resulting  from  the  processes 
of  conception,  constitute  the  material  which  may  possibly  form  the 
terms  of  judgments.  The  following  kinds  have  already  been  distin- 
guished :  (1.)  The  simple  notion,  called  also  simple  apprehension,  and 
percept.  This  is  the  result  of  immediate  cognitions  by  the  senses 
and  consciousness.  In  observation  this  notion  has  as  yet  no  name 
given,  but  may  be  known  by  the  indefinite  "  it."  An  orange,  as  an 
object  hitherto  unseen  and  unknown,  might  be  called  "it."  (2.)  The 
simple  abstract  notion,  or  part  abstracted  from  the  object  observed, 
but  not  yet  combined  with  others  into  a  concept.  By  observation  we 
get,  from  the  hitherto  unseen  and  uninvestigated  orange,  the  abstracts, 
yellow,  round,  sweet,  juicy,  etc.  (3.)  The  general  notion,  as  the  con- 
cept proper  or  bundle  of  properties  or  marks  expressed  in  the  concept 
term.  By  conception  proper  the  various  abstracted  properties  are 
gathered  up  in  thought  in  the  concept,  orange.  (4.)  The  general  no- 
tion, as  the  class  or  group  of  objects  to  which  the  bundle  of  attributes 
in  the  concept  applies.  By  classification  the  concept  orange  is  applied. 

It  will  be  seen  that  only  part  of  these  can  enter  into  the  strictly 
logical  judgment. 

II.  The  Connecting  Links  of  Judgment. 

The  two  terms  of  a  proposition  are  always  united  by  the 
copula,  which,  according  to  the  view  of  most  logicians,  is 
always  the  present  tense  indicative  of  the  verb  to  be,  either 
with  or  without  the  negative  particle.  The  real  quality  of 


THE   FORMATION   OF  JUDGMENTS.  95 

judgment,  however,  or  that  which  makes  it  what  it  is,  is 
the  mental  union  or  separation  of  two  terms  or  notions,  on 
the  ground  of  a  more  or  less  clearly  apprehended  connec- 
tion or  absence  of  connection  between  them.  The  various 
links  by  which  this  union  in  judgment  is  affected  are  to  be 
found  in  the  predicables  already  given. 

1.  While  the  connecting  link  of  judgment  in  language  is 
always  the  verb  to  be,  which  to  the  logician  signifies  connec- 
tion rather  than  existence,  it  is  obvious  that  the  copula  does 
not  always  appear  in  this  form  in  propositions  as  we  find 
them.     E.  g., 

"  Columbus  discovered  America  ;  "  "  Napoleon  was  the  emperor  of 
France."  Hence  arises  the  necessity  for  the  practical  application  of 
the  Second  Logical  Postulate,  in  reducing  judgments  to  the  normal 
form,  S  is  P,  or  S  is  not  P.  Under  this  any  change  of  logical  form  is 
permissible,  provided  it  brings  out  the  thought  more  fully,  without 
changing  it.  "I  am,"  means  "I  am  existing,"  or,  "I  am  a  being." 
"Columbus  discovered  America,"  means,  "Columbus  is  the  one  who 
discovered  America."  "  Napoleon  was  the  emperor  of  France,"  means, 
"  Napoleon  is  he  who  was  the  emperor  of  France."  "  Stars  twinkle," 
means,  "  Stars  are  things  that  twinkle."  The  same  postulate  permits 
the  restoration  of  all  inversions  and  displacements  of  parts  of  sen- 
tences to  the  normal  form,  S  is  P,  or  S  is  not  P.  E.  g.,  "  Great  is 
Diana  of  the  Ephesians  "  becomes  "  Diana  of  the  Ephesians  is  great." 

2.  A  judgment,  however,  is  not  a  mere  form  of  words, 
two  terms  joined  by  the  verb  to  be.     "  Man  is  intelligent." 
"  Man  is  round-square  horizontal."     One  of  these  is  a  judg- 
ment ;  the  other  is  not.     The  difference  is  that  in  the  one 
case  there  is  a  connection  in  thought,  while  in  the  other 
there  is  none.     This  connection  has  been  variously  pre- 
sented. 

(1.)  It  has  been  said  that  the  affirmative  judgment  is 
always  based  upon  the  Axiom  of  Identity  ;  the  negative  on 
the  Axiom  of  Contradiction.  In  accordance  with  this  view 
judgment  has  been  defined  to  be  the  affirmation  of  agree- 
ment or  disagreement. 


96  PRACTICAL    LOGIC. 

This  is  true,  but  it  is  necessary  to  go  below  these  generalities  to  the 
special  features  in  which  the  agreement  or  disagreement  is  found.  E. 
g.,  in  the  judgment,  "  Man  is  a  terrestrial,  rational  animal,"  the  copula 
represents  equality  or  identity.  This  is  true  in  all  perfect  definitions. 
Or  again,  in  the  judgment,  "  Man  is  intelligent,"  the  copula  expresses 
the  relation  of  substance  and  property,  or  genus  and  species,  and  the 
judgment  is  interpreted  as  meaning,  either  that  intelligence  is  an  attri- 
bute of  humanity,  or  that  man  is  a  species  of  the  genus  intelligent 
beings.  Or  again,  in  the  judgment,  "  The  life  was  the  light  of  men," 
the  copula  may  express  the  relation  of  substance  and  active  property 
or  cause  and  effect.  The  judgment  is  thus  seen  to  involve  certain  spe- 
cial principles  of  connection  which  underlie  the  mere  agreement  or 
disagreement. 

(2.)  According  to  the  Aristotelian  logic,  every  judgment  predicates 
of  the  subject  either  a  genus,  or  a  property,  or  a  definition,  or  an 
accident. 

These  forms  of  predication  have  been  illustrated  by  suitable  judg- 
ments. "  Envy  is  a  passion."  The  relation  is  that  of  genus  to  species. 
"Man  has  the  faculty  of  speech."  The  relation  is  that  si  peculiar 
property  to  substance  or  subject.  "A  state  is  a  community  governed 
by  its  own  laws."  The  relation  is  that  of  identity  of  the  essential 
properties,  or  essence  of  a  thing, —  by  which  the  definition  is  consti- 
tuted,— with  the  thing  itself.  "  Life  is  sweet."  The  relation  is  that 
of  an  accidental  property  to  its  subject. 

These  predicable  classes  have  been  reduced  by  Thomson  to  definition 
and  attribute,  the  latter  including  genus,  property,  and  accident. 

(3.)  The  Predicables  as  given,  page  30,  furnish  the  sim- 
plest statement  of  what  may  be  predicated  in  any  judgment. 
Of  any  subject  may  be  predicated  its  substance  and  what- 
ever belongs  to  it  as  its  properties. 

Thus  of  man  may  be  predicated  the  substance  of  the  thing  itself, 
as  "  Man  is  man ;  "  or  some  of  the  properties  of  quality,  as  "  Man  is 
rational,"  or  all  of  them  (the  essence  or  definition),  "Man  is  rational 
animal ;  "  or  active  properties,  as  "  Man  is  the  moulder  of  nature ;  "  or 
relative  properties,  as  "  Man  is  of  few  days,"  "  Man  is  terrestrial," 
"  Man  is  finite,"  etc. 

When  notions  or  terms  are  thought  together  by  one  or 
other  of  these  various  connections  the  product  is  a  judgment. 


THE   FORMATION   OF   JUDGMENTS.  97 

III.  The  Elements  Combined. 

The  various  notions  or  terms  are  united  either  in  judg- 
ments of  observation  or  in  strictly  logical  judgments. 
These  are  both  included  under  logical  judgments  in  the 
wider  sense. 

Note.— Hamilton  gives  the  name  of  primitive  judgment  to  the  judgment  of 
existence  implied  in  all  our  cognitions.  This  is  not,  however,  judgment  as  thought, 
and,  therefore,  is  not  to  be  treated  in  Logic. 

1.  The  judgment  of  observation  follows  upon  observation.     In  start- 
ing with  an  orange,  assumed  to  be  a  thing  never  before  known,  the 
observer  has  no  name  for  the  object.     The  mental  analysis  by  which 
the  abstracts  are  formed  may  be  looked  upon  as  made  up  of  a  succes- 
sion of  judgments  :  "  It  is  yellow  ;  "  "  It  is  sweet ;  "  "  It  is  round  ;  " 
etc.     All  the  predicates  of  these  judgments,  when  gathered  up,  give 
the  concept,  which  is  finally  embodied  in  the  word  orange,  and  then 
used  in  classifying  all  like  objects  as  oranges.     The  judgment  of  obser- 
vation may  be  seen  to  be  the  mental  union  of  simple  apprehensions 
or  percepts  and  abstracts. 

2.  The  judgment  of  observation  thus  prepares  the  way  for  and 
gradually  approaches  the  strictly  logical  judgment,  which  makes  use 
of  the  concept  and  class,  as,  "  The  orange  is  yellow ;  "  "  Oranges  are 
yellow."     It  will  readily  be  seen  that  the  strictly  logical  judgment 
will  take  different  forms,  as  the  subject  and  predicate  are  concept  or 
class  notions.     The  various  relations  of  the  notions  in  logical  judg- 
ments as  embodied  in  propositions  may  be  brought  out  in  the  following 
form,  using  the  notions  man  and  mortal: 

Subject.  Copula.  Predicate. 

Concept  proper,  Concept  proper, ' 

(Man  =  humanity)  r     is     -j          (mortal.) 

Class,  )      or     I  Class» 

(Man=.  mankind)  I  is  not'          (a  mortal.) 


The  strictly  logical  judgment  is  the  form  of  judgment  of 
which  Logic  mainly  treats.  In  the  logical  proposition  the 
two  terms  may  both  be  concept  terms,  giving  a  proposition 
of  content,  as,  "  Man  is  mortal ;  "  or  both  class  terms,  giv- 
ing a  proposition  of  extent,  as,  "  Man  is  a  mortal." 

The  subject  term  in  the  latter  form  may  be  either  an  individual,  as, 
9  G 


98  PRACTICAL    LOO  1C. 

"  Garibaldi ;  "  or  an  individualized  general  term,  as  "  this  man ;  "  or 
a  general  term  taken  partially,  as  "  some  men ; "  or  a  general  term 
taken  universally,  as  "  all  men."  This  form  of  logical  judgment  may, 
therefore,  be  either,  "  Garibaldi  is  a  mortal,"  or  "  This  man  is  a  mor- 
tal," or  "  Some  men  are  mortals,"  or  "  All  men  are  mortals." 

Note.— The  strictly  impersonal  judgments,  expressed  in  the  classical  lan- 
guages without  subject  (except  as  the  subject  in  the  third  person  singular  is 
involved  in  the  termination  of  the  impersonal  verb)  and  in  the  English  with 
"  it"  as  the  subject,  as,  "  it  rains,"  "  it  thunders,"  properly  come  under  the  logi- 
cal judgments.  Says  Ueberweg,  "  In  the  so-called  judgments  without  subjects 
the  sum  total  of  the  existence  surrounding  us,  thought  of  indefinitely,  or  an 
indefinite  part  of  it,  takes  the  place  of  the  subject." 

Praxis. — Examine  carefully  the  following  judgments,  stating  them 
in  the  normal  form  (S  is  P,  or  S  is  not  P),  naming  the  subject  and 
predicate,  and  bringing  out  the  precise  connecting  link  in  each  case : 
1.  Truth  is  stronger  than  error.  2.  The  human  race  was  one  in  its 
origin.  3.  A  square  is  rectangular.  4.  A  square  is  an  equilateral 
rectangle.  5.  "  Few  and  short  were  the  prayers  we  said."  6. 
"  Flashed  all  their  sabres  bare."  7.  Man  is  risible.  8.  Not  all  the 
ills  of  earth  can  mar  my  joy.  9.  Not  all  men  are  virtuous.  10.  A 
horse  may  be  white.  11.  He  that  destroys  a  usurper  does  right.  12. 
Great  is  the  work  of  life.  13.  There  was  no  possibility  of  substan- 
tiating the  allegations.  14.  "  In  jewels  and  gold  men  cannot  grow 
old."  15.  "  From  peak  to  peak  the  rattling  crags  among  leaps  the 
live  thunder."  16.  It  is  wrong  to  put  an  innocent  man  to  death. 
17.  There  is  no  place  like  home.  18.  "  None  but  the  brave  deserve 
the  fair."  19.  "  The  most  sublime  act  is  to  put  another  before  thee." 
20.  Life  every  man  holds  dear. 

Topic  Second. — Verification  or  Proof  of  Judgments. 

When  a  so-called  judgment,  expressed  in  a  proposition, 
is  brought  before  the  mind,  the  question  is  naturally  asked 
concerning  it,  What  reason  is  there  for  believing  it  to  be 
true?  A  so-called  judgment  is  decided  to  be  true,  doubt- 
ful, or  false,  by  the  presence  or  absence  of  proof,  i.  e.,  of 
something  which  makes  the  reality  of  the  connection  of  the 
two  notions  more  or  less  evident  to  the  mind. 

Practically,  in  all  our  intercourse  with  men  and  books,  judgments 
of  every  form  are  constantly  being  presented  to  our  minds  for  con- 


THE   FORMATION    OF  JUDGMENTS.  99 

sideration.  "  Geometry  is  the  science  of  extension."  "  Things  which 
are  equal  to  the  same  thing  are  equal  to  each  other."  "  Logic  is  the 
art  of  reasoning."  "  The  weather  is  cold."  "  If  the  weather  remains 
as  at  present,  the  streams  will  be  frozen  over."  In  short,  every  sen- 
tence read,  heard,  or  uttered  involves  one  or  more  judgments,  and  no 
such  judgment  is  anything  more  to  us  than  an  empty  assertion  until 
we  have  grasped  some  proof  that  the  expressed  connection  of  its  parts 
agrees  with  the  corresponding  reality.  The  verification  or  confirmation 
of  judgments  is,  therefore,  a  most  important  part  of  this  form  of  thought. 

Judgments  have  been  divided,  by  the  sources  from  which 
the  predicate  is  drawn,  into  analytic  and  synthetic.  The 
predicate  notion  may  either  be  brought  out  of  the  subject 
notion  by  analysis,  or  brought  to  it  from  without.  Proofs 
are  accordingly  either  analytic  or  synthetic,  the  former 
being  drawn  by  analysis  from  the  terms  of  the  proposition 
itself;  the  latter  being  brought  from  outside  the  terms  of 
the  proposition. 

An  analytic  or  explicative  judgment  is  one  in  which  what  is  affirmed 
in  the  predicate  is  already  contained  in  the  definition  of  the  concept 
or  general  term  which  forms  the  subject.  "  Man  is  rational,"  is  an 
analytic  judgment;  since  the  predicate,  rational,  is  involved  in  the 
notion,  man,  as  brought  out  by  partition  or  by  the  definition,  "Man 
is  a  rational  animal."  Such  judgments  are  also  called  a  priori,  or 
judgments  not  grounded  on  but  prior  to  experience.  The  simple  study 
of  what  is  contained  in  the  subject  notion  gives  the  predicate  without 
resort  to  the  testimony  of  experience.  E.  g.,  in  the  judgment,  "  Body 
is  extended,"  the  instant  the  thinker  understands  what  is  meant  by  the 
term  "body,"  he  knows  that  "extended"  is  comprehended  in  it.  A 
synthetic  or  ampliative  judgment  is  one  in  which  the  predicate  adds 
something  which  is  not  contained  in  the  conception  or  definition  of  the 
subject.  E.  g.,  "Man  is  a  sinner,"  "Neptune  is  the  most  remote  of 
the  planets,"  are  synthetic  judgments.  The  predicate  adds  to  the 
subject  something  which  it  brings  from  outside  and  which  no  analysis 
could  have  discerned  in  the  subject. 

In  connection  with  the  various  forms  of  judgment  analytic 
and  synthetic  the  nature  of  the  proof,  and  the  canons  or 
rules  governing  it,  will  be  set  forth. 


100  PRACTICAL    LOGIC. 

I.  Proof  of  Analytic  Judgments. 

Analytic  judgments  furnish  within  themselves  the  ma- 
terial for  their  own  verification.  This  is  to  be  brought  out 
by  analysis,  i.  e.,  by  partition  or  division  of  the  subject  or 
predicate  or  both. 

The  proposition,  "All  trees  are  organic,"  is  proved  by  analyzing 
"  organic."  The  proposition  is  regarded  as  one  of  extent,  affirming 
that  the  genus,  "  organic  beings  "  includes  the  species,  "  trees."  Or- 
ganic beings  are  divided,  by  the  presence  or  absence  of  a  nervous  sys- 
tem and  power  of  causation,  into  animals  and  plants.  Plants  are 
divided,  by  the  size  and  duration  of  the  stem  or  ascending  axis,  into 
herbs,  shrubs,  and  trees.  The  result  reached  may  be  expressed  in  tab- 
ular form : 

Organic  beings  =  j  Animals,       /  Herbs, 
(  Plants     =  |  Shrubs, 
( Trees ; 

froDi  which  it  is  apparent  that  the  lower  species  "  trees  "  is  included 
under  the  higher  genus  "  organic."  The  proposition,  "  Duelling  is 
murder,"  is  analytic.  Regarded  as  a  proposition  of  content,  its  proof 
is  reached  by  partition  of  the  terms.  "  Murder  "  includes  the  generic 
mark,  taking  of  human  life,  and  the  differential  or  specific  marks,  de- 
liberately, unlawfully,  maliciously.  "Duelling,"  where  it  results  in 
death,  is  found  to  include  the  same  marks,  taking  of  human  life,  de- 
liberately, unlawfully,  maliciously.  The  two  are  thus  found  to  agree. 
Duelling  is,  therefore,  murder,  i.  e.,  the  relation  affirmed  to  exist  between 
the  two,  in  the  proposition  to  be  proved,  corresponds  to  the  reality. 
The  proof  of  the  proposition,  "Labor  is  a  blessing  to  man,"  is  to  be 
found  by  an  analysis  of  the  terms.  Regarded  as  a  proposition  of  ex- 
tent, it  affirms  that  "labor"  is  one  species  of  the  genus  or  class 
"blessings  to  man."  By  partition  "blessing  to  man"  has  the  active 
properties  or  characteristics,  meeting  some  fundamental  and  natural 
need  of  man,  giving  satisfaction  or  happiness.  There  are,  therefore,  as 
many  "blessings  to  man  "  as  he  has  fundamental  and  legitimate  needs 
to  be  satisfied.  Analyzing  "  blessings  to  man  "  by  division,  we,  there- 
fore, find  that  the  genus  includes  the  desires  for  habitual  activity 
physical  and  rational,  for  knowledge,  for  power,  for  property,  for  help 
in  dependence  and  helplessness,  for  deliverance  from  sin,  etc.  Any- 
thing which  meets  and  satisfies  any  one  of  these  desires  is  a  blessing 


THE  FORMATION   OF   JUDGMENTS.        101 

to  man.  "  Labor "  analyzed  by  partition  is  found  to  include  the 
marks,  exertion  of  the  powers,  habitual,  with  rational  aim,  or,  in  other 
words,  habitual  rational  activity.  "  Labor,"  as  meeting  the  funda- 
mental and  legitimate  need  for  habitual  rational  activity  is  a  "  blessing 
to  man."  Continuing  the  process  of  thought  still  further,  we  may 
conclude  from  the  analysis,  that  "  knowledge  "  is  a  blessing  to  man, 
"power"  is  a  blessing  to  man,  "wealth"  is  a  blessing  to  man,  "the 
sustaining  power  of  divine  providence"  is  a  blessing  to  man,  "sal- 
vation from  sin  "  is  a  blessing  to  man,  etc. 

General  Rule. — The  analysis  must  be  accurate  and  com- 
plete. 

It  is  obvious  that  this  method  of  proof  must  render  cer- 
tain the  truth  of  the  propositions  which  admit  of  its  appli- 
cation. All  analytic  proof  is,  therefore,  said  to  be  demon- 
strative in  its  force. 

II. — Proof  of  Synthetic  Judgments. 

Synthetic  judgments  require  that  their  proofs  be  sought 
outside  of  the  judgments  themselves.  No  analysis  of  terms 
will  furnish  the  proof  that,  "  Duelling  is  a  relic  of  barbar- 
ism," or  that,  "  The  Feudal  System  was  beneficial."  The 
proof  must  be  brought  from  outside  sources. 

The  precise  source  or  place  outside  will  depend  upon  the 
species  of  synthetic  judgment  to  be  proved.  Synthetic 
judgments  are  divided,  by  the  place  outside  the  proposition 
from  which  the  predicate  is  brought,  into  intuitive  and  em- 
pirical. 

Intuitive,  or  a  priori,  judgments  are  those  whose  predicates  are 
brought  from  within  the  mind  itself,  from  some  fundamental  or  thought 
necessity.  In  these  the  predicate  could  never  be  unfolded  from  the 
subject,  as  in  the  judgment,  "  Every  event  must  have  a  cause."  It  is 
a  law  of  our  thinking  that  compels  us  to  connect  "  must  have  a  cause  " 
with  the  subject,  "  every  event."  Empirical,  or  a  posteriori,  judg- 
ments are  those  of  which  the  predicates  are  brought  from  outside  the 
mind.  They  have  their  ground  in  experience.  The  judgment,  "  Body 
is  extended  substance,"  is  analytic,  since  "  extended  substance  "  is  seen 
to  be  comprehended  in  "body,"  or  to  be  identical  with  it;  but  the 


102  PRACTICAL    LOGIC. 

judgment,  "  Body  is  heavy,"  is  a  synthetic  judgment,  since  the  mark 
"heavy  "  is  not  comprehended  in  "  body."  The  latter  is  an  empirical 
judgment,  since  only  experience,  examining  bodies  and  measuring 
pressure  by  muscular  effort,  enables  us  to  predicate  "  heavy  "  of  "  body." 

1.  Proof  of  Intuitive  Judgments.  —  These  draw  their 
proofs  from  the  mind  itself.  The  proofs  are  intuitions  or 
fundamental  truths,  accepted  by  all,  and  lying  at  the  foun- 
dation of  all  human  knowledge  and  activity. 

For  the  proposition,  "  Suicide  is  wrong,"  the  proof  is  to  be  found 
in  man's  intuitive  convictions  of  duty.  Every  one  knows  intuitively 
that  man,  as  a  creature  under  the  moral  government  of  God,  is  bound 
to  make  the  most  and  the  best  of  himself,  and  that  to  fail  in  this  is 
wrong.  Duty  is  intuitively  seen  to  require  that  he  should  preserve 
himself,  improve  himself,  and  use  his  powers  for  the  true  end  of  life. 
"Suicide"  is  intuitively  seen  to  break  the  first  of  these  requirements, 
and,  therefore,  seen  to  be  "  wrong."  The  propositions,  "  I  exist,"  "  I 
am  thinking,"  rest  upon  the  intuitive  belief  in  the  veracity  of  our 
consciousness. 

As  so-called  intuitions  are  often  urged  in  proof  of  various 
false  judgments,  it  becomes  necessary  to  keep  clearly  in 
mind  the  tests  of  intuition,  These  may  be  given  in  the 
following  rules : 

Rule  1st. — Every  intuition  is  self-evident.  The  mind,  on  the  bare 
contemplation  of  it,  must  see  its  truth  at  once,  without  requiring  any 
foreign  evidence  or  outside  proof. 

Rule  2d. — Every  intuition  is  necessary.  The  mind  cannot  help  be- 
lieving and  acting  upon  its  truth.  That  "  Space  exceeds  my  widest 
imagination  of  space,"  and  that  "  Every  event  must  have  a  cause," 
one  cannot  help  believing. 

Rule  3d. — Every  intuition  is  catholic  or  universal.  It  must  be  en- 
tertained by  all  men  intelligent  and  understanding  what  is  meant  by 
it.  An  intuition  is  sometimes  described  as  being  "  What  all  men 
everywhere  and  always  believe." 

Rule  4th. — Every  intuition  is  accepted  by  all  men  practically.  In- 
tuitive truths  may  not  be  consciously  apprehended  and  stated  by  the 
majority  of  mankind,  but  they  are  assumed  and  acted  upon  by  all 
men,  even  by  those  who  deny  their  belief  in  them. 


THE    FORMATION    OF   JUDGMENTS.         103 

The  notions  of  being,  personal  identity,  time,  space,  causation,  the 
axioms  of  Mathematics,  Logic,  Ethics,  etc.,  are  among  these  self-evi- 
dent, necessary,  and  universal  cognitions  of  men. 

It  is  evident  that  all  such  proofs,  properly  tested,  must 
render  certain  the  truth  of  propositions  based  upon  them. 
Intuitive  proofs  are,  therefore,  said  to  be,  like  analytic 
proofs,  demonstrative  in  force. 

2,  Proofs  of  Empirical  Judgments.  —  Empirical  judg- 
ments, or  those  based  upon  something  outside  of  the  propo- 
sition and  of  the  mind  itself,  rest  for  their  proofs  upon  the 
experience  of  the  thinker  himself  or  of  others.  Knowledge 
in  the  form  of  experience  has  been  seen  (p.  16)  to  include 
the  observation  and  thinking  of  the  man  himself,  and  the 
observation  and  experience  of  others  given  in  testimony 
and  authority.  This  suggests  the  kinds  of  empirical  judg- 
ments to  be  established. 

(1.)  Judgments  from  Observation. — When  the  judgment  to  be  veri- 
fied is  based  upon  our  own  observation  of  things  external  or  internal, 
its  truth  is  tested  by  careful  application  of  the  Rules  of  Observation 
already  given  (p.  33).  Thus,  "  I  see  my  uplifted  hand  in  all  its  parts ; " 
"  I  am  conscious  of  exertion  in  lifting  my  hand,"  are  judgments  of 
observation.  Their  truth  evidently  depends  upon  the  trustworthiness 
of  the  senses  and  consciousness,  assumed  in  all  observation,  and  upon 
strict  compliance  with  the  Rules  of  Observation. 

(2.)  Judgment  from  Thought.  —  Many  empirical  judgments  are 
reached  by  the  processes  of  Reasoning  Inductive  and  Deductive. 
These  must  be  tested  by  the  Canons  of  Reasoning,  which  will  be 
presented  in  Part  III. 

(3.)  Judgments  from  Testimony  and  Authority. — Testi- 
mony is  the  statement  of  others  concerning  matters  of  fact 
which  they  have  observed  in  their  own  consciousness  or  in 
the  world  around  them.  Authority  is  the  statement  of 
others  concerning  matters  of  opinion  which  they  have 
reached  by  the  processes  of  conception,  judgment,  and  rea- 
soning. The  testimony  or  authority  may  be  recorded  on 


104  PRACTICAL    LOGIC. 

monuments  or  in  writings,  books,  etc.,  or  given  by  word  of 
mouth. 

As  almost  all  human  knowledge  is  received  on  testimony 
or  authority,  the  question,  What  are  the  tests  of  testimony 
and  authority  ?  becomes  a  most  important  one.  The  tests 
are  to  be  found  either,  first,  in  the  ability,  character  and 
number  of  witnesses  or  authorities,  or,  secondly,  in  the 
character  of  that  which  they  present.  Out  of  these  arise 
the  Rules  to  be  observed  in  judging  of  the  truth  or  falsity 
of  judgments  received  from  others. 

Rule  1st. — A  witness  or  authority  must  be  competent, 
i.  e.,  must  have  the  opportunity,  the  ability,  and  the  dispo- 
sition to  know  the  facts  testified  to,  or  to  think  out  the 
judgments  presented  on  his  authority. 

a.  Want  of  opportunity  to  observe  destroys  the  value  of  any  so- 
called  testimony.     The  testimony  of  A  concerning  what  B  says  that  C 
did  is  mere  hearsay,  and  of  little  evidential  value.     Negative  testi- 
mony is  of  little  value.     The  testimony  of  a  thousand  witnesses  that 
they  did  not  see  A  kill  B  is  not  sufficient  to  countervail  the  statement 
of  one  good  witness  that  he  did  see  A  kill  B.     Want  of  ability  to  ob- 
serve the  facts  in  any  given  case  may  make  the  testimony  worthless. 
A  blind  man's  testimony  to  mere  objects  of  sight  is  worthless.     Cer- 
tain spheres  of  observation  require  special  skill,  so  that  only  the  testi- 
mony of  experts,  or  those  trained  for  the  purpose,  may  be  of  value 
in  those  spheres.    A  man  acquainted  with  the  phenomena  of  electricity 
will  be  able  to  detect  important  facts  which  would  entirely  escape  the 
notice  of  the  ordinary  observer.     Testimony  regarding  the  distance, 
size,  form,  and  appearance  of  any  object  requires  a  trained  judgment 
to  make  the  observation  trustworthy.     Thus  the  testimony  of  an  ex- 
pert,—  e.  g.,  of  a  practical  astronomer  to  the  fall  of  a  meteor, —  may 
become  of  more  value  than  that  of  hundreds  of  ordinary  observers. 
Want  of  disposition  to  observe  accurately  vitiates  testimony.     This 
may  result,  through  habitual  carelessness,  in  imperfect  observation,  or, 
through  prejudice,  in  warped  views  of  things.     There  are  men  who, 
from  the  first  cause,  never  see  anything  worth  seeing,  and  others  who, 
from  the  second  cause,  always  see  things  double  or  quadruple  or  as 
they  expect  or  wish  to  see  them. 

b.  Want  of  opportunity  or  ability  or  disposition  to  think  out  the 


THE   FORMATION    OF  JUDGMENTS.         105 

conclusions  for  which  one  is  quoted  as  an  authority  must,  of  course, 
destroy  the  weight  of  the  authority.  In  order  to  be  an  authority  in 
any  department  of  thought  a  man  must  have  had  special  opportunity 
of  acquaintance  with  that  department,  must  have  shown  himself  pos- 
sessed of  extraordinary  ability  to  deal  with  it  and  of  unusual  mastery 
of  it,  and  must  be  disposed  to  seek  and  discern  the  truth  in  it.  The 
authorities  in  Law  are  the  men  who  have  shown  themselves  masters 
of  legal  science.  The  authorities  in  Physical  Science,  are,  accord- 
ing to  Professor  Tait,  "  the  advanced,  best,  ablest  scientific  thinkers." 
The  "competent  authorities  ""  in  Physics  are  not  the  men  who  simply 
observe  and  experiment,  but  the  men  of  exact  science,  who,  largely  by 
the  aid  of  mathematics,  have  advanced  the  bounds  of  the  science. 
Professor  Tait  names  as  such  authorities  in  Great  Britain,  "  Brewster, 
Faraday,  Forbes,  Graham,  Rowan  Hamilton,  Herschel,  and  Talbot," 
in  the  immediate  past,  and  "Andrews,  Joule,  Clerk  Maxwell,  Balfour 
Stewart,  Stokes,  William  Thomson,  and  such  like,"  in  the  present.  The 
authorities  in  Theology,  Philosophy,  etc.,  are  the  men  who  are  masters 
in  these  departments. 

The  utterance  of  a  competent  authority  in  any  department  has  great 
weight  even  when  not  accompanied  with  the  reasons,  because  he  is 
rightly  supposed  to  know  whereof  he  affirms.  The  word  of  the  aver- 
age man,  even  if  he  is  admitted  to  be  familiar  with  his  subject,  has 
just  as  much  weight  as  the  reasons  by  which  he  supports  it,  and  it  has 
weight  at  all  only  as  he  presents  his  reasons  along  with  it.  He  is  not 
an  authority.  Assertions  made  concerning  Theology,  Metaphysics, 
etc.,  by  experimental  physicists  who  have  given  absolutely  no  attention 
to  those  difficult  departments,  are  worth  just  as  much  as  the  counter 
assertions  made  concerning  Experimental  Physics  by  theologians  who 
know  nothing  of  that  department.  In  all  such  cases,  however  dis- 
tinguished a  man  may  be  in  his  own  department,  his  words  concerning 
the  unknown  department  should  have  only  so  much  weight  as  is  given 
by  the  reasons  with  which  he  accompanies  them. 

Rule  2cL — A  witness  or  authority  must  be  credible,  i.  e.t 
must  be  of  such  a  character  as  to  be  worthy  of  belief. 

a.  Whatever  the  opportunities  or  natural  ability  of  a  witness,  if 
he  is  shown  to  be  careless  in  observing,  credulous  in  receiving  state- 
ments, addicted  to  falsehood,  under  the  influence  of  prejudice,  or 
swayed  by  motives  that  would  warp  his  view  of  the  facts,  the  value 
of  his  testimony  is  just  so  far  impaired. 


106  PRACTICAL    LOGIC. 

b.  The  value  of  arthority  is  equally  affected  by  the  credibility  of 
the  one  giving  the  opinion.  If  the  judge  who  renders  a  certain  de- 
cision can  be  shown  to  be  corrupt,  or  to  be  in  any  way  wanting  in 
principle,  his  decision  will  come  so  far  short  of  commanding  assent  as 
authority. 

Rule  3d. — Concurrence  in  testimony  or  authority  in- 
creases the  probability  of  its  truth. 

a.  The  force  of  concurrence  in  testimony  is  broken  when  there  is 
evidence  of  collusion  or  pre-arrangement.     Precise  agreement  in  stat- 
ing the  general  facts  and  all  the  details  of  any  occurrence  is  looked 
upon  as  proof  of  collusion ;  whereas  incidental  variation  in  non-essen- 
tial particulars,  along  with  general  agreement,  shows  the  absence  of 
collusion  and  the  truthfulness  of  the  witnesses.     Where  there  has  been 
no  opportunity  for  collusion,  concurrent  testimony  may  become  abso- 
lutely conclusive  even  where  all  the  witnesses  are  noted  liars.     In 
such  cases  we  cannot  account  for  the  agreement  except  on  the  ground 
that  what  the  witnesses  independently  state  is  true. 

b.  The  force  of  concurrence  in  authority  is  subject  to  the  same  limi- 
tations as  that  in  testimony.     Too  precise  agreement  in  statement  of 
matters  of  opinion  indicates  probable  collusion.     No  weight  is  to  be 
attached  to  the  concurrence  of  many  judges,  if  it  can  be  shown  that 
the  successive  decisions  have  all  followed  some  one  original  and  lead- 
ing decision.     If,  however,  there  is  evidence  that  each  arrived  at  his 
decision  by  independent  thought,  the  authority  may  become  of  the 
greatest  weight,  even  when  the  word  of  each  one  separately  could 
command  little  or  no  respect.     The  cumulative  force  of  convergent 
evidence  or  argument  is  also  to  be  considered.     The  convergence  of 
several  lines  of  proof  is  often  sufficient  to  render  certain  what  perhaps 
no.one  of  these  lines  alone  would  fully  establish.     This  is  illustrated 
in  the  proof  that  there  is  a  personal  God.     The  consent  of  mankind, 
the  principle  of  causation,  the  order  of  the  universe,  the  intuition  of 
the  infinite,  the  voice  of  conscience,  and  the  yearnings  of  the  affections, 
all  converge  towards   the  common  centre,  a  personal  God,  and  the 
strength  of  the  proof  lies  in  this  convergence,  rather  than  in  the  sep- 
arate arguments  taken  alone. 

Rule  4th. — Things  absurd  or  impossible  are  not  to  be  be- 
lieved on  the  ground  of  testimony  or  authority,  although 


THE   FORMATION    OF   JUDGMENTS.         107 

things  strange,  wonderful,  or  even  miraculous  may  be  be- 
lieved on  such  ground. 

Whatever  is  absurd  or  impossible,  i.  e.,  logically  contradictory  or 
beyond  the  reach  of  power  to  accomplish,  cannot,  of  course,  be  believed. 
No  testimony  or  authority  could  make  one  believe  in  a  triangle  with 
four  sides,  or  in  Mill's  conceived  world  in  which  two  and  two  make 
five.  It  must  be  observed,  however,  that  what  is  merely  contrary  to 
experience  is  not  necessarily  absurd  or  impossible.  The  King  of  Siam 
had  never  in  his  experience  known  water  to  be  transformed  into  a 
solid  upon  which  men  could  walk ;  but  every  one  sees  that  this  was 
not  sufficient  reason  for  his  pronouncing  the  missionary,  who  told  him 
of  such  a  thing,  a  liar  and  impostor,  since  human  experience  is  very 
limited. 

There  is  need  to  note  especially  the  natural  inclination  of  men  to 
pronounce  everything  absurd  and  impossible  which  contradicts  their 
settled  convictions,  their  preconceptions  or  their  prejudices,  or  which 
is  repugnant  to  their  feelings.  It  was  once,  by  the  majority  of  man- 
kind, pronounced  impossible  for  the  earth  to  turn  on  its  axis  and  move 
through  space  with  incredible  rapidity  without  our  perceiving  it.  It 
was  declared  absolutely  impossible  that  information  should  be  trans- 
mitted thousands  of  miles  in  the  fraction  of  a  second,  or  that  a  man 
should  converse  with  his  friend  hundreds  of  miles  away.  It  must  be 
borne  in  mind  that  the  impossible  is  only  that  which  is  logically  con- 
tradictory or  beyond  the  reach  of  power ;  and  that,  therefore,  before 
any  particular  thing  can  be  pronounced  impossible,  the  laws  and  limi- 
tations of  thought  and  power  must  be  comprehended  and  found  to 
forbid  its  accomplishment.  A  thing  may,  therefore,  be  perfectly  cred- 
ible, though  it  be  strange,  unaccountable,  or  even  unintelligible. 
"  What  is  strange  or  unaccountable  to  one  mind  may  be  perfectly 
familiar  and  plain  to  another.  For  the  most  limited  intellect  or  ex- 
perience to  make  itself  the  standard  of  the  possible,  would  be  as  absurd 
as  a  man's  making  his  visible  horizon  the  limit  of  space."  Even  tes- 
timony to  supernatural  and  miraculous  events  may  be  entirely  worthy 
of  belief,  if  there  be  any  Supernatural  Power  in  the  universe,  and 
such  events  may  and  ought  to  be  believed  if  the  witnesses  are  com- 
petent and  credible  and  concur  in  their  statements.  It  is  a  remarkable 
fact  that  the  greatest  scientists  and  philosophers, — such  men  as  Bacon, 
Locke,  Descartes,  Newton,  Herschel,  Brewster,  and  Faraday, — have 
unhesitatingly  believed  in  miracles  on  the  ground  of  such  testimony, 
regarding  them,  not  as  events  without  any  adequate  cause,  but  as 


108  PRACTICAL    LOGIC. 

events  into  whose  production  a  higher,  Unseen  Cause  entered.  In  all 
such  cases,  however,  the  witnesses  to  the  supernatural  events  should 
be  subjected  to  the  most  rigid  scrutiny  and  cross-examination,  accord- 
ing to  the  established  rules  of  testimony. 

It  is  evident  that  the  proofs  of  empirical  judgments  never 
give  the  judgments  the  absolutely  demonstrative  force  which 
belongs  to  the  proofs  of  analytic  and  intuitive  judgments, 
but  simply  render  them  more  or  less  probable.  As  the 
entire  practical  ongoing  of  human  life  depends  upon  such 
judgments  from  experience,  i.  e.,  from  observation,  thought, 
testimony,  and  authority,  the  meaning  and  truth  of  Butler's 
statement,  that  "probability  is  the  guide  of  life,"  becomes 
apparent. 

Probability  varies  in  different  cases.  It  may  in  one  case  practically 
amount  to  certainty ;  in  another  the  balance  may  be  as  a  thousand,  or 
a  million,  or  vastly  more,  to  one,  against  the  truth  of  the  judgment. 
The  rational  conduct  of  human  affairs  varies  accordingly.  Where 
the  balance  of  probabilities  is  in  favor  of  the  truth  of  a  judgment, 
men  base  their  action  upon  it,  in  all  the  ordinary  affairs  of  life,  with 
a  confidence  increasing  as  the  degree  of  probability  rises.  When  the 
probabilities  are  as  fifty-one  to  forty-nine  that  certain  goods  will 
greatly  advance  in  price,  the  enterprising  merchant  hesitatingly  in- 
vests in  them  ;  as  the  probabilities  become  as  seventy-five  to  twenty- 
five,  he  invests  more  eagerly ;  as  the  probabilities  approach  certainty, 
he  secures  control  of  all  that  his  capital  will  enable  him  to  command. 
Where  great  and  permanent  practical  interests  are  involved,  even 
the  lowest  degree  of  probability  should,  in  accordance  with  the  dic- 
tates of  common  sense,  be  acted  upon.  The  man  wrecked  in  mid- 
ocean  wisely  clings  to  his  solitary  plank  even  when  the  probabilities 
that  he  will  be  saved  are  only  as  one  to  a  thousand  or  even  one  to  a 
million.  The  balancing  of  probabilities  and  deciding  the  course  in 
view  of  them  is  manifestly  an  essential  part  of  man's  rational  and 
moral  discipline  in  this  world. 

Note. — Professor  Jevons  says  of  the  Theory  of  Probabilities :  "  It  is  the  very 
guide  of  life,  and  hardly  can  we  take  a  step  or  make  a  decision  of  any  kind 
without  correctly  or  incorrectly  making  an  estimate  of  probabilities.  .  .  .  The 
whole  cogency  of  inductive  reasoning  rests  upon  probabilities.  The  truth  or 
untruth  of  a  natural  law,  when  carefully  investigated,  resolves  itself  into  a 


THE   FORMATION    OF   JUDGMENTS.        109 

high  or  low  degree  of  probability,  and  this  is  the  case  whether  or  not  we  are 
capable  of  producing  precise  numerical  data."— Jevons'  Principles  oj  Science, 
p.  217. 

Praxis. — Examine  critically  the  following  judgments  or  proposi- 
tions,—  first,  stating  of  each  whether  it  is  analytic  or  synthetic ; 
secondly,  if  analytic,  developing  the  proof  from  the  judgment  itself; 
thirdly,  if  synthetic,  showing  whence  its  proofs  are  to  be  derived  and 
bringing  the  proofs  of  the  judgments  from  observation,  testimony,  and 
authority  from  the  proper  sources : 

1.  Washington  is  the  capital  of  the  United  States. 

2.  George  Washington  was  a  true  patriot. 

3.  Columbus  discovered  America. 

4.  New  Orleans  is  situated  on  the  Mississippi. 

5.  England  is  across  the  Atlantic  Ocean. 

6.  There  is  such  a  country  as  China. 

7.  Madagascar  is  inhabited. 

8.  Civilization  has  been  progressive  from  the  earliest  ages. 

9.  The  Aztecs  reached  a  high  degree  of  civilization. 

10.  Lying  is  never  justifiable. 

11.  The  Allegheny  Mountains  were  formerly  submerged. 

12.  The  Himalayas  are  the  highest  mountains  on  the  globe. 

13.  The  feudal  system  was  beneficial. 

14.  Honesty  is  the  best  policy. 

15.  Education  cannot  be  effected  by  mere  class-room  instruction  or 
lecturing. 

16.  The  sum  of  the  three  angles  of  a  triangle  is  equal  to  two  right 
angles. 

17.  Two  straight  lines  cannot  inclose  a  space. 

18.  The  earth  is  between  93,000,000  and  94,000,000  miles  from  the 
sun. 

19.  Wrong-doing  blinds  the  conscience. 

20.  Falsehood  is  dangerous. 

21.  The  story  of  Christ's  life  and  death  is  true. 

22.  Joan  of  Arc  was  a  religious  enthusiast. 

23.  In  a  right-angled  triangle  the  hypothenuse  is  the  longest  side. 

24.  Any  two  sides  of  a  triangle  are  together  greater  than  the  third. 

25.  Christianity  is  of  divine  origin. 

26.  The  study  of  the  classics  is  necessary  to  the  highest  culture. 

27.  North  America  was  once  inhabited  by  a  race  of  Indians  of 
higher  civilization  than  the  existing  tribes. 

10 


110  PRACTICAL    LOGIC. 

28.  Christianity  is  the  religion  which  meets  the  needs  of  man. 

29.  A  triangle  cannot  have  more  than  one  angle  as  great  as  a  right 
angle. 

30.  The  moon  revolves  round  the  earth. 

31.  The  best  science  recognizes  a  God. 

32.  Probability  is  the  guide  of  life. 

Section  II,— The  Products  of  Judgment, 
The  process  of  judging  results  in  judgments  which  are 
embodied  in  propositions.  These  products  need  to  be  care- 
fully classified  and  divided,  since  the  unfolding  of  judg- 
ments depends  upon  a  knowledge  of  their  kinds  and  char- 
acteristics, and  since  judgments  constitute  the  material  of 
Reasoning,  the  third  Form  of  Thought. 

Judgments  of  content  and  extent  and  analytic  and  syn- 
thetic judgments  have  already  been  considered  in  treating 
the  process  of  judgment  (pp.  97-99).  For  further  logical 
purposes  the  chief  divisions  of  judgments  are  based  on  the 
various  ways  of  making  the  predication  or  assertion,  since 
the  assertive  element  is  the  main  one  in  judgment.  This 
gives  rise  to  the  following  divisions : 

First,  by  the  quality  of  the  predication,  whether  affirmative  or  not, 
into  affirmative  and  negative  judgments.  This  division  is  treated 
under  Quality  of  Judgments. 

Second,  by  the  extent  of  the  predication,  whether  total  or  not,  into 
universal  or  total  and  particular  or  partial  judgments.  This  division 
is  treated  under  Quantity  of  Judgments. 

Third,  by  the  directness  of  the  predication,  whether  direct  or  indi- 
rect, into  categorical  and  hypothetical.  This  division  is  treated  under 
Relation  of  Judgments. 

Fourth,  by  the  degree  of  certainty  of  the  predication,  whether 
certain  or  not,  into  certain  including  demonstrative  and  assertory,  and 
not-certain  including  probable  and  possible.  This  division,  as  it  has 
reference  to  the  results  in  the  mind  of  the  thinker  himself,  will  be 
treated,  in  summing  up  the  results  of  thinking  in  its  second  form,  at 
the  close  of  Part  II.,  under  Modality  of  Judgments. 

Since  the  divisions  of  scientific  syntax  in  Grammar  depend  upon  the 
forms  and  combinations  of  logical  judgments  or  logical  propositions, 


THE   FORMATION    OF   JUDGMENTS.         Ill 

for  grammatical  purposes  there  is  still  another  division  of  judgments, 
which  needs  to  be  considered : 

Fifth,  by  combination,  whether  single  or  not,  into  simple,  and  mul- 
tiple or  combined  including  complex  and  compound.  This  is  treated 
under  Grammatical  Combination  of  Judgments. 

Topic  First. — Quality  of  Judgments. 

By  the  quality  or  character  of  the  predication  judgments 
are  either  affirmative,  as,  "  Belgium  is  populous;  "  or  nega- 
tive, as,  "  The  vicious  are  not  wise."  In  the  former  there 
is  indicated  the  union  of  the  two  notions  by  some  link  of 
connection,  and  they  are,  therefore,  said  to  agree,  by  the 
principle  of  Identity  ;  in  the  latter  there  is  indicated  by  the 
negative  the  separation  of  the  two  notions,  which  are,  there- 
fore, said  to  disagree,  by  the  principle  of  Contradiction. 

It  follows  from  the  nature  of  negation  that  a  negative  copula  always 
excludes  everything  in  the  predicate, — the  whole,  the  species,  the  indi- 
viduals,— entirely  from  the  subject.  E.  g.,  "  No  men  are  angels"  cuts 
off  the  entire  class  "  angels  "  and  all  that  is  included  in  it  from  the 
class  "men."  "Some  men  are  not  artists"  cuts  off  the  entire  class 
"  artists  "  from  these  "  some  men."  This  is  called  the  distribution  of 
the  predicate,  or  the  taking  of  it  in  its  entire  signification. 

It  should  be  observed  that  the  negative  particle  is  not  always  con- 
nected with  the  copula,  but  may  be  placed  in  other  parts  of  the  propo- 
sition ;  yet  in  every  judgment  really  negative  it  belongs  only  to  the 
copula.  By  the  second  Logical  Postulate  it  is  always  permissible  to 
put  the  negative  into  its  proper  place,  with  the  verb  to  be,  in  reducing 
any  proposition  to  the  normal  form,  S  is  not  P.  "  No  human  knowl- 
edge is  perfect "  may  thus  be  changed  into,  "  All  human  knowledge 
is  not  perfect."  In  many  apparently  negative  propositions  the  force 
of  the  negative  particle  does  not  fall  on  the  copula,  but  upon  one  of  the 
terms.  E.  g.,  "Not  to  submit  is  madness  "  is  really  an  affirmative  prop- 
osition, since  the  force  of  the  "not"  falls  on  the  words  "to  submit." 
The  meaning  is,  "Non-submission  (or  resistance)  -is  madness."  Again, 
"A  person  not  vicious  is  virtuous"  is  equivalent  to,  "A  non-vicious 
person  is  virtuous,"  and  is,  therefore,  an  affirmative  proposition.  In 
like  manner  propositions  apparently  affirmative  may  be  really  nega- 
tive, the  force  of  the  negative  particle  being  in  some  way  involved  in 
the  thought,  if  not  in  the  form  of  expression.  E.  g.,  "  Only  a  few 


112  PRACTICAL    LOGIC. 

men  are  wise  ;  "  "  Few  men  are  wise ; "  "  But  few  men  are  wise,"  are 
all  substantially  negative  propositions,  since  they  are  equivalent  to, 
"  Most  men  are  not  wise."  On  the  other  hand,  "  A  few  men  are  wise," 
is  an  affirmative  proposition.  Great  care  should  manifestly  be  exer- 
cised in  ascertaining  the  precise  quality  of  all  such  propositions. 

Topic  Second. — Quantity  of  Judgments. 

The  quantity  of  judgments  depends  upon  the  extent  of 
the  predication.  Certain  logical  distinctions,  which  arise 
from  the  combination  of  quantity  with  quality,  may  also 
be  most  conveniently  treated  under  this  Topic. 

I.  Kinds  of  Judgments  by  Quantity. 

The  predicate  notion  of  a  judgment  may  be  affirmed  or 
denied  either  of  the  whole  of  a  subject  or  of  a  part  of  it 
only.  Having  once  formed  the  notion,  "orange,"  we  may 
affirm  that,  "This  orange  is  yellow,"  or,  "Some  oranges 
are  yellow,"  or,  "All  oranges  are  yellow."  Hence  judg- 
ments by  this  division  are  universal  or  total  and  particular 
or  partial. 

1.  Universal  or  total  judgments  include  the  strictly  uni- 
versal, or  those  in  which  the  notion  of  the  subject  is  taken 
in  its  entire  extent ;  the  judgments  in  which  a  definite  part 
of  the  notion  of  the  subject  is  taken;  the  judgments  with 
individualized,  singular,  or  collective  subjects ;  and  equiv- 
alent or  substitutive  judgments. 

Universal  judgments  in  the  strict  sense  are  those  in  which  the  pred- 
icate notion  is  affirmed  or  denied  of  the  entire  subject  notion,  i.  e.,  of 
all  that  is  comprehended  or  contained  under  it,  whether  attributes  or 
objects.  The  subject  is,  in  this  case,  a  logical  whole  taken  in  all  its 
parts.  "All  men  are  mortal;"  "Every  man  is  mortal,"  are  univer- 
sal judgments,  the  subject  embracing  the  total  number  of  objects  in  the 
class  "man."  The  subject  in  all  universal  judgments,  whether  affirm- 
ative or  negative,  is  said  to  be  distributed,  because  what  is  predicated 
is  predicated  of  each  and  every  object  in  the  entire  whole.  Universal 
judgments  include  those  in  which  a  definite  part  of  the  subject  is  taken, 
as,  "These  men  are  Japanese."  They  also  include  judgments  with 
individualized  subjects,  as,  "  This  man  is  sober ;  "  and  judgments  with 


THE   FORMATION    OF   JUDGMENTS.         113 

singular  subjects,  as,  "Bucephalus  is  a  horse;"  "France  is  not  an 
empire."  This  follows  from  the  fact  that  the  predicate  notion  is  af- 
firmed or  denied  of  the  whole  subject.  The  same  is  true  of  judgments 
whose  subjects  are  collective  wholes,  as  army,  forest;  mass  wholes, 
as,  wheat,  rice ;  material  wholes,  as  gold,  stone. 

From  the  predication  of  the  definition,  or  essence,  of  a  notion,  there 
arises  a  peculiar  kind  of  universal  judgment  in  which  the  subject  and 
predicate  are  equal  and  identical.  This  is  known  as  the  equivalent,  or 
substitutive  judgment,  in  distinction  from  the  simple  attributive  judg- 
ment or  ordinary  universal.  For  example,  "  Body  is  extended  sub- 
stance ; "  "  Man  is  a  rational  animal."  In  all  such  judgments  the 
notions  or  terms  of  both  subject  and  predicate  are  taken  in  their  entire 
meaning,  or  distributed. 

The  signs  of  universal  judgments  are  all,  every,  each,  both,  any,  none, 
neither,  always,  never,  whoever,  wherever,  whatever,  etc.  Care  must  be 
taken,  however,  to  guard  against  the  ambiguous  use  of  such  signs, 
especially  against  such  use  of  the  word  all.  The  word  all  in  its  proper 
logical  sense  means  "  each  and  every ; "  but  it  stands  sometimes  for 
"all  taken  together,"  as,  "All  these  claims  upon  my  time  overpower 
me."  Hence  may  arise  an  ambiguity,  since  instead  of  all,  in  its  proper 
sense  of  "all  taken  together,"  we  are  liable,  in  our  interpretation,  to 
put  all  in  its  logical  sense  of  "  each  and  every."  The  example  could 
not  mean,  "  Every  single  claim  upon  my  time  overpowers  me." 

2.  Particular  or  partial  judgments  embrace  the  ordinary 
form  including  the  purely  indefinite  and  the  semi-definite 
judgments;  and  the  more  unusual  forms  called  numerically 
definite  and  plurative  judgments. 

Particular  or  partial  judgments  are  those  in  which  the  predicate 
notion  is  affirmed  or  denied  of  a  number  of  objects  less  than  the  whole 
denoted  by  the  subject  notion,  as,  "Some  men  are  poets,"  "Some  rulers 
are  not  just."  In  particular  judgments  the  naked  subject  must  always 
be  restricted  either  by  implication  or  by  some  restrictive  term.  The 
signs  of  particular  judgments,  are,  some,  not  all,  not  every,  a  few,  there 
are — that,  a  or  an,  one,  two,  three,  etc.,  sometimes,  somewhere,  etc. 

The  word  some,  as  used  in  introducing  particular  judgments  embod- 
ied in  propositions,  is,  as  Hamilton  has  shown,  ambiguous.  In  some 
instances  it  introduces  a  semi-definite  judgment,  as,  "  Some  men  are 
poets,"  i.  e.,  some  at  most,  not  all.  In  other  instances  it  introduces  a 
strictly  indefinite  judgment,  as,  "Some  men  reason,"  i.  e.,  some  at 
10*  H 


114  PRACTICAL    LOGIC. 

least,  perhaps  all  The  latter  is  the  old  logical  meaning  of  some,  and 
the  judgment  is  wholly  indefinite ;  the  former  meaning  makes  the  judg- 
ment semi-definite,  since  it  excludes  all.  In  which  sense  the  word  is 
used  in  any  given  instance  must  be  determined  by  examining  the 
thought  or,  in  connected  discourse,  the  context.  Numerically  defi- 
nite judgments,  are  those  in  which  the  predicate  notion  is  affirmed 
or  denied  of  a  definite  number  or  proportion  of  the  objects  included 
in  the  subject,  as,  "  Ten  men  in  a  thousand  are  wise."  Considering 
the  "  ten  men  "  alone  as  the  subject,  the  judgment  would  be  regarded 
as  universal,  since  the  predicate  is  affirmed  of  all  the  ten.  Of  like 
nature  are  plurative  judgments  which  embrace  more  than  half  but 
not  all  the  subject.  These  may  be  numerically  definite,  as,  "  Forty 
men  out  of  the  fifty  on  the  steamer  perished ;  "  or  indefinite,  as,  "  Most 
men  are  not  poets."  In  the  numerically  definite  form  the  sign  is  found 
in  numbers  expressing  more  than  half  of  the  whole  embraced  in  the 
subject.  In  the  indefinite  plurative  judgment  the  signs  are  found  in 
such  expressions  as,  more  than  half,  the  majority,  many,  etc. 

"When  the  predication  approaches  more  nearly  to  covering  the  whole 
of  the  subject,  as  in  approximately  universal  judgments,  such  terms 
are  used  as  most,  almost  every  one,  the  large  majority,  etc.  On  the 
other  hand  the  following  signs  are  nearly  total  negatives :  few,  very 
few,  hardly  or  scarcely  any,  little,  small,  slight,  rare,  seldom,  etc. 

II.  Logical  Distinctions  from  Quantity  and  Quality  Com- 
bined. 

Two  subjects — the  normal  forms  of  judgments  as  they 
appear  in  the  syllogism,  and  the  distribution  of  terms — are 
dependent  upon  both  Quality  and  Quantity,  and  will  be 
most  naturally  treated  and  best  understood  in  immediate 
connection  with  these  topics. 

1.  Normal  Forms  of  Judgment. — Men  in  their  thinking 
combine  quality  and  quantity  in  judgments.  To  facilitate 
the  use  of  judgments  in  the  syllogism  logicians  have  formed 
a  complete  scheme  of  judgments  combining  quality  and 
quantity,  and  have  affixed  to  each  form  a  symbol  by  which 
both  quality  and  quantity  are  briefly  expressed.  The  pos- 
sible combinations  are  four,  two  of  which  are  subdivided  as 
shown  in  the  following  form : 


THE   FORMATION    OF   JUDGMENTS.         115 

Quantity.     Quality.  Symbol.                 Formula. 

Universal  Affirmative, 

Attributive,  A,  All  S  is  (some)  P. 

[  Substitutive,  U,  All  S  is  (all)  P.] 

Universal  Negative,  E,  No  S  is  (any)  P. 
Particular  Affirmative, 

•§           Attributive,  I,  Some  S  is  (some)  P. 

[  Substitutive,  Y,  Some  S  is  (all)  P.] 

Particular  Negative,  0,  Some  S  is  not  (any)  P. 

These  may  be  illustrated  by  examples: 

All  men  are  (some)  mortals  ....  A. 

[  All  men  are  (all)  rational  animals  .  .  .  U.} 

No  men  are  (any)  angels     .  E. 

Some  men  are  (some)  mortals  ....  I. 

[  Some  men  are  (all)  the  poets  Y.] 

Some  men  are  not  (any)  artists  ...  0. 

The  judgments  in  most  common  use  are  A,  E,  I,  and  0,  and  the  log- 
ical processes  are  usually  confined  mainly  to  these. 

2.  Distribution  of  Terms. — As  already  indicated,  a  term 
is  said  to  be  distributed  when  it  is  taken  in  its  entire  sig- 
nification embracing  each  and  every  object  included  under 
it.  From  the  principles  already  presented  a  general  state- 
ment of  the  terms  distributed,  or  taken  in  their  full  extent, 
in  the  various  judgments  and  also  of  those  undistributed, 
or  not  taken  in  their  full  extent,  can  readily  be  made. 
These  may  be  embodied  in  Rules. 

Rule  1st. — All  universals, — A,  U,  and  E, — and  no  par- 
ticulars,— I,  Y,  and  0,- — distribute  the  subject. 

Rule  2d. — All  negatives, — E  and  0, — and  all  substitutive 
affirmatives, — U  and  Y, — but  no  attributive  affirmatives, — 
A  and  I, — distribute  the  predicate. 

From  the  nature  of  quantity  and  quality,  as  seen  in  the  statements 
made  and  examplep  given,  it  appears  that  the  six  kinds  of  judgment* 
have  their  terms  distributed  or  undistributed,  as  follows : 


116  PRACTICAL    LOGIC. 

A  distributes  the  subject  only. 

U          "          both  subject  and  predicate. 

E          "          both  subject  and  predicate. 

I  "          neither  subject  nor  predicate. 

Y          "          the  predicate  only. 

0          "  the  predicate  only. 

Praxis. — State  of  each  of  the  following  judgments, — first,  to  which 
of  the  six  forms  it  belongs,  and  whether  its  terms  are  distributed  or 
undistributed  and  why,  marking  the  judgment  by  its  appropriate 
letter ;  secondly,  if  the  judgment  is  particular,  whether  it  is  definite, 
semi-definite,  numerically  definite,  plurative,  etc.,  and  if  universal, 
whether  singular,  attributive,  substitutive,  etc.;  and,  thirdly,  if  am- 
biguous, wherein  the  ambiguity  consists : 

1.  All  oaks  are  trees.  2.  Some  men  have  genius.  3.  Poets  are  men 
of  genius.  4.  Body  is  extended  substance.  5.  This  inkstand  is  made 
of  glass.  6.  The  senate  has  adjourned.  7.  Birds  breathe  and  fly.  8. 
"  All  Jerusalem  went  out  to  meet  him."  9.  Salt  is  chloride  of  sodium. 
10.  Some  men  reason.  11.  Some  men  seek  reputation.  12.  A  few  were 
saved.  13.  He  that  does  not  heed,  stumbles.  14.  Nine  boys  out  of  ten 
prefer  play  to  study.  15.  Forty  of  the  fifty  sailors  perished.  16.  Not 
every  mistake  is  culpable.  17.  Milton  was  blind.  18.  All  men  are 
not  liars.  19.  God  is  good.  20.  Gold  is  a  heavy  metal.  21.  With  rare 
exceptions  men  are  selfish. 

Topic  Third.— Relation  of  Judgments. 

The  relation  of  judgments  depends  upon  the  manner  of 
predication.  The  predication  may  be  made  either  simply 
and  positively  or  may  be  made  to  depend  upon  something 
else.  The  first  gives  rise  to  the  categorical  judgment ;  the 
second  to  the  hypothetical. 

Note.— The  ordinary  grammatical  division  of  propositions  as  embodied  in 
sentences  is  based  upon  the  mental  states  embodied.  It  embraces  the  follow- 
ing kinds  of  sentences : 

/Expressing  Cognition  or  Intellect,  including,— 

I    (  Interrogative,  showing  search  for  ground  of  judgment, 
m\l   Hypothetical,  showing  certain  grounds  only  as  still  in  doubt, 
8  1  (  Categorical,  showing  the  comparison  and  connection  completed ; 
v  /Expressing  Emotion  or  Sensibility, — 
g  J      Exclamatory,  embodying  feeling ; 
w  /Expressing  Conation  or  Will,  including, — 

I    (  Optative,  indicating  wish  or  choice, 

V  1  Imperative,  indicating  determination  or  volition. 


THE  FORMATION   OF   JUDGMENTS.        117 

Interrogative  sentences  may  have  the  same  terms  as  the  other  sentences  ex- 
pressing cognition,  and  are  treated  in  Logic  in  the  same  manner  as  those  sen- 
tences. The  elements  of  emotion  and  will  do  not  enter  into  the  thought  of  the 
proposition,  in  the  strict  sense.  In  so  far  as  the  sentences  based  upon  them  ex- 
press thought  in  the  proper  sense,  they  may  be  treated  as  propositions  express- 
ing cognitions,  and  so  become  either  categorical  or  hypothetical.  See  Davis' 
Logic,  p.  82. 

1.  A  categorical  judgment  is  one  in  which  the  predicate 
is  affirmed  or  denied  of  the  subject  simply  and  absolutely 
or  without  condition,  as,  "  Captain  Jack  was  a  Modoc  chief;  " 
"  Benedict  Arnold  was  not  a  patriot."     The   affirmatives 
are  based  on  the  principle  of  Identity,  the  negatives  on 
that  of  Contradiction. 

2.  A  hypothetical  judgment  is  one  in  which  the  predica- 
tion  is   based   upon   some  circumstance  "  which  must  be 
granted  or  supposed  before  the  assertion  becomes  applicable." 
The  supposition  may  be  either  a  condition  or  an  alternative 
or  both  these  combined ;  and  hypothetical  judgments  are, 
therefore,  of  three  kinds,  conditional,  disjunctive,  and  di- 
lemmatic. 

(1.)  A  conditional  or  conjunctive  judgment  suspends  the  predication 
upon  some  supposed  circumstance  (called  a  condition),  as,  "  If  the  sun 
shines  the  snow  melts."  This  may  be  put  into  the  form,  "  The  snow 
is, — if  the  sun  shines, — melting."  "  Melting  "  is  predicated  of  "  snow  " 
upon  the  condition  that  "  the  sun  shines."  If  it  be  true  that  "  the 
sun  shines,"  then  it  is  true  that  "  the  snow  melts."  The  supposed  cir- 
cumstance, "  If  the  sun  shines,"  is  called  the  antecedent ;  the  judg- 
ment suspended  upon  the  condition  is  called  the  consequent.  The  rela- 
tion between  the  two  is  that  of  reason  and  consequent,  or  cause  and 
effect.  The  conditional  judgment  is,  therefore,  based  upon  the  princi- 
ple of  Sufficient  Reason.  The  signs  of  conditionals  are,  if,  when,  in 
case  of,  etc. 

Conditional  judgments  may  be  converted  into  categorical  form  by 
changing  the  signs,  if,  when,  in  case  of,  etc.,  into  such  phrases  as  "the 
case  of,"  "  the  circumstances  in  which,"  etc.  Thus  the  conditional, 
"  If  the  sun  shines  the  snow  melts,"  becomes  "  The  case  of  the  sun's 
shining  is  the  case  of  the  snow's  melting." 

(2.)  A  disjunctive  judgment  suspends  the  predication  upon  some 
alternative  introduced  by  "either — or."  It  involves  two  or  more 


118  PRACTICAL    LOO  I C. 

judgments,  all  of  which  cannot  be  true,  but  one  or  more  of  which,  by 
the  principle  of  Excluded  Middle,  must  be  true.  Thus  in  the  disjunc- 
tive, "  Either  the  Bible  is  false  or  holiness  ought  to  be  followed,"  there 
are  two  alternative  judgments,  "  The  Bible  is  false;  "  and  "  Holiness 
ought  to  be  followed."  "  Either  London  is  in  England  or  it  is  not," 
contains  two  alternative  judgments,  "  London  is  in  England; "  "  Lon- 
don is  not  in  England."  One  or  other  of  them  must  be  true ;  the 
other  cannot  be.  The  disjunctive  needs  to  be  carefully  distinguished 
from  the  partitive  judgment,  which,  under  the  form  of  a  disjunctive, 
simply  predicates  of  a  genus  its  several  species ;  as,  "  All  Africans  are 
either  bond  or  free."  The  genus,  Africans,  is  in  this  case  made  up  of 
the  component  species,  bond  and  free,  which  are  affirmed  of  it  not 
alternatively  nor  disjunctively,  but  concurrently.  The  affirmation  of 
the  one  is  not  a  denial  of  the  other. 

Disjunctive  judgments  may  be  converted  into  categorical  form  by 
using  all  their  members  for  one  of  the  terms,  and  the  phrase  "  possible 
cases,"  or,  "  the  only  alternative,"  or  one  like  it,  for  the  other  term. 
The  disjunctive,  "  This  season  is  either  Spring,  Summer,  Autumn,  or 
Winter,"  becomes,  "  All  the  possible  cases  regarding  this  season  are 
Spring,  Summer,  Autumn,  and  Winter."  Disjunctives  may  also  be 
converted  into  conditionals  by  taking  the  contradictory  of  one  of  the 
members  for  the  antecedent  and  making  the  other  members  conse- 
quents. Thus,  "If  it  is  not  Summer,  it  is  either  Autumn,  Winter,  or 
Spring." 

(3.)  A  dilemmatic  judgment  is  a  hypothetical  involving  a  combina- 
tion of  the  conditional  and  the  disjunctive.  The  disjunctive  may  fall 
either  in  the  antecedent  or  in  the  consequent.  Thus,  "  If  a  man  falls 
into  the  sea,  he  will  either  sink  or  swim  ;  "  "  If  man  is  either  praise- 
worthy or  blameworthy,  he  must  be  a  free  agent." 

A  dilemmatic  judgment  may  be  converted  into  categorical  form  by 
changing  each  of  its  elements,  according  to  the  principles  laid  down 
under  hypotheticals  and  disjunctives. 

Topic  Fourth.— Grammatical  Combination  of  Judgments 
or  Propositions. 

Judgments  embodied  in  propositions  are  either  single  or  combined. 
Combined  judgments  are  combined  by  subordination  or  by  co-ordina- 
tion. Propositions  are,  therefore,  simple,  complex,  or  compound. 

A  simple  proposition  consists  of  only  one  subject  and  predicate.  Both  the 
subject  and  predicate  may,  however,  be  grammatically  very  complex,  e.  g.,  "A 


THE   FORMATION    OF   JUDGMENTS.          119 

legitimate  and  forcible  argument  may  fail  to  win  the  assent  of  a  prejudiced 
man."  The  kinds  of  judgments  thus  far  treated  are  chiefly  forms  of  simple 
judgments  embodied  in  simple  propositions. 

A  complex  proposition  consists  of  a  principal  judgment  with  one  or  more 
subordinate  judgments,  e.  g.,  "  Man  who  is  born  of  a  woman  is  of  few  days." 
The  subordinate  elements  appear  as  substantive,  adjective,  or  adverbial  elements, 
so  that  in  logic  the  complex  sentence  is  treated  as  embodying  a  simple  judg- 
ment. The  office  of  the  subordinate  clauses  is  explicative,  as,  "  Whoever  is 
right,  is  safe ; "  or  restrictive,  as,  "  Men  who  are  avaricious  are  discontented." 

A  compound  proposition  is  made  up  of  two  or  more  co-ordinate  judgments,  as, 
"  Art  is  long,  and  time  is  fleeting."  For  logical  purposes  the  constituent  judg- 
ments of  a  compound  proposition  require  separate  and  independent  statement. 
Co-ordination  is  either  copulative,  adversative,  disjunctive,  or  causal.  The  co- 
ordination is  copulative  when  two  or  more  thoughts,  which  are  considered 
independent,  are  so  united  together  that  the  thought  expressed  in  the  co-ordi- 
nated judgment  gives  a  greater  extent  to  the  thought  of  the  preceding  judg- 
ments, e.  g.,  "  Socrates  and  Plato  were  wise ;  "  "  Plato  was  a  philosopher  and 
Sophocles  was  a  poet."  The  copulative  connection  may  be  either  annexive,  en- 
hansive,  intensive,  or  ordinative.  The  co-ordination  is  adversative  when  the 
judgments  united  in  thought  stand  in  opposition  to  one  another,  e.  g.,  "Not 
the  rich  are  happy,  but  the  good."  The  opposition  may  be  contradictory,  con- 
trary, or  restrictive.  The  co-ordination  is  disjunctive  when  the  judgments 
united  in  the  one  thought  exclude  one  another,  e.  g.  "  Either  he  is  here  or  he 
is  not  here."  The  disjunction  is  either  exclusive  as  in  the  ordinary  disjunctive 
judgments,  or  separative  as  in  comparisons.  The  co-ordination  is  causal  when 
the  last  of  the  co-ordinate  judgments  denotes  the  ground  of  the  preceding  judg- 
ment, or  the  conclusion  from  it,  as,  "  Aristotle  was  an  accurate  thinker,  for  he 
formed  conceptions  and  judgments  well."  The  causal  relation  in  the  wide 
sense,  may  be  either  reason,  or  cause  proper,  or  conclusion  from  reason,  or  conse- 
quence from  cause. 

Note. — For  a  full  presentation  of  the  principles  of  subordination  and  co-or- 
dination, see  Kiihner's  Latin  and  Greek  Grammars,  and  Becker's  German 
Grammar. 

Praxis. — Examine  and  characterize  the  following  judgments, — First, 
reducing  them  to  the  normal  form ;  secondly,  bringing  out  the  connect- 
ing links;  thirdly,  indicating  the  sources  of  proof;  fourthly,  giving 
the  quantity,  quality,  and  relation,  and  showing  the  distribution  of 
the  terms ;  fifthly,  stating  whether  simple  or  combined,  and  if  com- 
bined showing  whether  complex  or  compound,  and  bringing  out  the 
particular  relations  of  subordination  or  co-ordination : 

1.  No  reptiles  have  feathers. 

2.  Grace  is  unmerited  favor. 

3.  None  are  free  who  do  not  govern  themselves. 

4.  He  that  ruleth  his  own  spirit  is  greater  than  he  that  taketh  a 
city. 

5.  George  Eliot  was  the  wife  of  George  H.  Lewes. 


120  PRACTICAL    LOGIC. 

6.  He  that  getteth  silver  is  not  satisfied  with  silver. 

7.  Thomas  Jefferson  prepared  the  first  Anglo-Saxon  Grammar  pro- 
duced in  America. 

8.  There  is  no  fireside,  howsoe'er  defended, 
But  has  one  vacant  chair. 

9.  Never  morning  wore  to  evening  but  some,  heart  did  break. 

10.  The  rich  are  not  necessarily  happy,  for  happiness  is  not  the 
result  of  external  circumstances. 

11.  Those  here  present  constitute  the  class  in  Logic. 

12.  All  that  glitters  is  not  gold. 

13.  Man  was  originally  a  long-eared  animal  of  arboreal  habits. 

14.  A  miracle  is  impossible. 

15.  No  such  thing  as  a  miracle  has  ever  been  experienced. 

16.  Who  steals  my  purse,  steals  trash. 

17.  Life  every  man  holds  dear. 

18.  If  Christ  rose  from  the  dead,  then  Christianity  is  true. 

19.  Either  Richard  III.  was  a  monster  or  Shakespeare  was  wrong. 

20.  If  Socrates  was  innocent,  Anytus  was  either  deceived  or  per- 
jured. 

21.  Wherever  thore  is  smoke,  there  is  fire. 

22.  If  Caesar  lives,  he  will  rule  or  ruin. 

23.  He  would  have  gone,  but  was  prevented  by  sickness. 

24.  Goliath  uttered  his  challenge  and  David  accepted  it. 

25.  First,  the  dawn ;  then,  the  rising  sun ;  and  last,  the  busy  tide 
of  life. 

26.  There  are  studies  much  vaunted,  yet  of  little  utility. 

27.  Some  democracies  are  unstable. 

28.  Some  honest  men  become  bankrupt. 

29.  The  world's  no  neuter ;  it  will  wound  or  save. 

30.  The  country  is  generally  flat  or  but  slightly  undulating. 

31.  Wealth  may  seek  us  ;  but  wisdom  must  be  sought. 

32.  He  had  the  air  of  dignity,  yet  of  deep  feeling. 

33.  For  man  to  tell  how  human  life  began  is  hard ;  for  who  him- 
self beginning  knew  ? 

34.  Thy  father  slew  my  father  ;  therefore  die. 

35.  We  have  no  slaves  at  home — then  why  abroad  ? 

36.  He  is  very  great  in  knowledge,  and  accordingly  valiant. 

37.  I  have  the  wish,  but  want  the  will  to  act. 

38.  The  widow  and  her  child  returned  to  England,  and  lived  almost 
hopeless  in  their  old  home. 


THE    UNFOLDING    OF   JUDGMENTS.        121 

CHAPTER  II. 
THE  UNFOLDING  OP  JUDGMENTS. 

THE  best  use  of  judgment  in  the  practical  work  of  think- 
ing requires  that  the  thinker  should  be  able  to  unfold  what 
may  be  contained  in  any  judgment,  or  implied  in  it,  or  im- 
mediately inferred  from  it.  Hence  the  following  Topics: 

First,  the  development  of  contained  judgments. 
Second,  the  development  of  implied  judgments. 
Third,  the  development  of  inferred  judgments. 

Note.— Some  logicians  consider  this  subject  as  a  part  of  Reasoning.  Ac- 
cording to  these,  Reasoning  is,  either  by  inference  from  one  judgment  to  an- 
other derived  from  it ;  or  from  two  judgments  to  a  third,  which  could  not  be 
derived  from  either  alone  but  is  drawn  from  both  combined.  The  latter  is 
called  Mediate  Inference ;  the  former  Immediate  Inference.  The  subjects  of 
the  present  Chapter  are,  according  to  this  view,  treated  under  the  head  of  Rea- 
soning. They  are,  however,  properly  to  be  treated  under  Judgment,  for  they 
all  flow  from  the  nature  of  conceptions  as  already  presented  and  from  the  re- 
lations of  these  conceptions  in  judgments  and  propositions. 

Section  I,— Development  of  Contained  Judgments, 
That  which  is  contained  in  any  judgment  may  be  brought 
out  by  analysis  of  the  content  or  extent  of  its  terms,  the 
subject  and  predicate. 

This  form  of  analysis  is  of  great  service  in  careful  thinking  and 
especially  in  confirmation  of  judgments.  It  is  applicable,  of  course, 
only  to  judgments  in  which  at  least  one  of  the  terms  is  complex  or 
has  component  attributes  or  species.  The  process  must  conform  to  the 
laws  of  Partition  and  Division. 

The  proposition,  "  The  highest  civilization  is  dependent  on  Chris- 
tianity," may  be  analyzed,  as  a  proposition  of  content,  either  by  par- 
tition of  the  subject  or  of  the  predicate.  The  subject,  "the  highest 
civilization,"  includes  as  marks  or  attributes :  the  most  righteous  civil 
government ;  the  completest  development  of  the  arts  industrial  and 
aesthetic ;  the  broadest  and  most  liberal  education  ;  the  best  manners 
and  morals,  or  conduct  in  all  relations ;  the  highest  spirit  of  enter- 
prise and  progress.  The  proposition  may  therefore  be  unfolded  into 
the  following :  The  most  righteous  civil  government  is  dependent  on 
11 


122  PRACTICAL   LOGIC. 

Christianity ;  The  completest  development  of  the  arts  industrial  and 
aesthetic  is  dependent  on  Christianity ;  The  broadest  and  most  liberal 
education  is  dependent  on  Christianity  ;  The  best  form  of  manners  and 
morals,  or  conduct,  in  all  relations  is  dependent  on  Christianity ;  The 
highest  degree  of  enterprise  and  progress  is  dependent  on  Christianity. 
The  predicate  element,  "  Christianity,"  may  be  analyzed  to  meet  the 
requirements  of  these  propositions  for  proof.  From  this  point  of  view, 
it  includes  the  following  marks :  the  perfect  standard  of  justice ;  the 
true  theory  of  activity  and  beauty ;  the  grandest  system  of  truth ; 
the  complete  theory  of  responsibility  and  duty ;  the  inspiring  prin- 
ciples of  progress.  The  proposition  may,  therefore,  be  unfolded  into  the 
following :  The  highest  civilization  is  dependent  upon  Christianity  as 
a  perfect  standard  of  justice ;  The  highest  civilization  is  dependent 
upon  Christianity  as  the  true  theory  of  activity  and  beauty;  The 
highest  civilization  is  dependent  on  Christianity  as  embracing  the 
grandest  system  of  truth  ;  The  highest  civilization  is  dependent  on 
Christianity  as  the  complete  theory  of  responsibility  and  duty ;  The 
highest  civilization  is  dependent  on  Christianity  as  containing  the  in- 
spiring principles  of  progress. 

Propositions  of  extent  may  be  unfolded  by  the  principles  of  division. 
Thus,  "  Free  institutions  are  conducive  to  progress,''  may  be  unfolded 
through  the  subject  as  a  genus,  as  including  free  governmental  institu- 
tions,, free  educational  institutions,  free  social  institutions,  free  religious 
institutions,  etc. ;  and  through  the  predicate,  as  including  political  prog- 
ress, educational  progress,  social  progress,  religious  progress,  etc. 

To  the  development  of  contained  judgments  manifestly  belongs  also 
what  Thomson  names,  "  Immediate  Inference  by  the  Sum  of  several 
Predicates."  "Copper  is  a  metal,  red,  malleable,  ductile,  etc.,"  is  in 
no  proper  sense  an  immediate  inference  from  the  judgments,  "  Copper 
is  a  metal,"  "  Copper  is  red,  etc.,"  but  a  simple  compounding  of  them. 
So  these  component  judgments  are  simple  constituents  of  the  general 
judgment,  and  may  be  unfolded  from  it. 

Praxis. — Develop  the  following  propositions  by  Subject  and  Pred- 
icate, and  suggest  the  sources  of  proof  for  the  resulting  propositions: 

1.  The  studies  of  the  High  School  Course  are  best  fitted  to  prepare 
for  the  pursuits  of  business  life. 

2.  The  studies  of  the  College  Course  are  best  fitted  to  prepare  for 
the  work  of  the  professions. 

3.  The  Fine  Arts  are  favorable  to  a  pure  morality. 


THE    UNFOLDING    OF   JUDGMENTS.         123 

4.  The  study  of  the  Ancient  Classics  is  the  best  discipline  for  the  mind. 

5.  Manly  qualities  are  becoming  to  a  student. 

6.  Proper  protection  of  the  various  industries  is  essential  to  national 
prosperity. 

7.  The  discipline  of  life  is  essential  to  man's  development. 

8.  Division  of  labor  is  essential  to  national  wealth. 

Section  II,— Development  of  Implied  Judgments, 
The  implied  judgment,  according  to  Davis,  "  is  one  that 
actually  exists  together  with  the  given  judgment,  either 
merely  in  thought  or  involved  covertly  in  the  expression." 
Several  simpler  and  less  important  forms  of  implication 
need  to  be  noted,  but  especially  the  more  important  form 
named  obversion. 

Topic  First— Simpler  Forms  of  Implication. 

These  are  chiefly  forms  of  interpretation  of  the  language 
or  thought. 

Such  judgments  may  be  covertly  implied  in  the  language.  Thuc, 
in  the  proposition,  "  Few  men  are  wise,"  it  is  covertly  implied  by  the 
language  that  "  Most  men  are  not  wise."  "  Some  men  are  rich,"  im- 
plies that  "  Some  men  are  not  rich."  Such  judgments  are  sometimes 
implied  in  the  thought.  Thomson  places  under  immediate  inference, 
what  he  names,  "  Immediate  Inferences  of  Interpretation."  It  is  not 
strictly  inference  but  rather  implication.  Thus,  in  the  judgment,  "  John 
loves  Mary,"  it  is  implied  that  "  John  lives,"  that,  "Mary  lives,"  and 
that,  "  there  is  such  a  thing  as  love." 

.  The  development  of  active  and  passive  forms  of  judgments  from 
each  other  may  also  be  placed  here.  In  the  active  form,  "  Napoleon 
conquered  Europe,"  is  implied  the  passive  form,  "  Europe  was  con- 
quered by  Napoleon." 

In  any  simple  proposition  many  other  propositions  may  be  implied. 
Thus,  "  Yesterday  I  lifted  one  hundred  pounds,"  implies  judgments 
of  the  existence  of  yesterday,  of  the  one  hundred  pounds,  of  myself,  of 
the  lifting,  6f  memory,  of  time,  of  personal  identity,  of  will  power,  etc. 

Topic  Second, — Obversion. 

Under  implied  judgments  belongs  also  what  Bain  calls 
obversion.  It  is  sometimes  termed,  "  Immediate  Inference 


124  PRACTICAL    LOGIC. 

by  Reciprocal  Change  of  Positive  and  Privative  Concep- 
tions." In  affirming  one  thing  we  impliedly  deny  the  op- 
posite. Obversion  is  the  bringing  out  and  denying  of  this 
opposite  or  reverse  form. 

Thus,  "  The  road  is  level ;  "  "  The  road  is  not  inclined ;  "  are  not 
two  facts,  but  the  same  fact  from  different  sides.  The  second  is  not  an 
inference  from  the  first,  but  something  implied  in  the  first, — an  obverse 
form  of  the  first.  "Whoever  is  wise  is  not  foolish  ;  "  we  must  grant 
the  obverse  form  if  we  grant  the  positive.  In  obversion  the  negative 
form  may  be  taken  either  as  infinitated  or  as  simply  privative.  "  Wise  " 
implies  the  infinitated  notion,  "  not-wise  "  or  "  non-wise,"  the  two  to- 
gether making  up  the  universe  of  being ;  and  also  the  privative,  "  not- 
wise  "  or  "  unwise." 

Each  of  the  normal  forms  of  judgment, — A,  E,  I,  0, — 
has  its  obverse  form.  For  developing  these  obverse  implied 
judgments  we  have  the  following 

Rule. — Obvert  the  predicate  (i.  <?.,  change  it  to  the  infin- 
itated or  privative  form)  and  then  change  the  quality  of  the 
judgment. 

Note.— To  avoid  awkward  compounds  with  non  and  not,  in  obverting  and 
changing  the  quality  of  judgments,  various  prefixes  and  suffixes  are  often  used, 
as,  in-,  un-,  dis-,  less-,  etc. ;  and  uncompounded  negatives,  as  unwise  and  foolish, 
instead  of  not- wise.  Great  care  needs,  however,  to  be  taken,  as  these  terms 
are  often  not  privatives,  but  only  signify  the  existence  of  the  quality  in  a  low 


Taking  the  four  principal  judgments  as  embodied  in 
propositions,  in  the  order  of  the  letters  representing  them, 
and  applying  the  Rule  given  above,  we  get  the  obverse 
forms : 

1.  The  normal  form  of  the  universal  affirmative,  A,  is  as  follows: 
Every  x  is  y;  Every  man  is  mortal. 
Obverting  the  predicate,  this  becomes : 

Every  x  is  not-y  ;  Every  man  is  (not-mortal)  immortal. 
Changing  the  quality  of  the  judgment  from  affirmative  to  negative, 
it  becomes : 

No  x  is  not-y ;  No  man  is  (not-mortal)  immortal. 


THE    UNFOLDING    OF   JUDGMENTS.         125 

2.  The  normal  form  of  the  universal  negative,  E,  is  as  follows :  No 
x  is  y ;  No  men  are  angels. 

Obverting  the  predicate,  this  becomes : 

No  x  is  not-y  ;  No  men  are  not-angels. 

Changing  the  quality  of  the  judgment  from  negative  to  affirmative, 
it  becomes : 

Every  x  is  not-y  ;  All  men  are  not-angels  (excluded  from  angels). 

3.  The  normal  form  of  the  particular  affirmative,  I,  is  as  follows : 
Some  x  is  y  ;  Some  men  are  wise. 

Obverting  the  predicate,  this  becomes : 

Some  x  is  not-y;  Some  men  are  (not-wise)  foolish. 

Changing  the  quality  of  the  judgment  from  affirmative  to  negative,  it 

becomes : 

Some  x  is  not  not-y ;  Some  men  are  not  foolish. 

4.  The  normal  form  of  the  particular  negative,  0,  is  as  follows : 
Some  x  is  not  y ;  Some  men  are  not  wise. 

Obverting  the  predicate,  this  becomes : 

Some  x  is  not  not-y ;  Some  men  are  not  (not-wise)  unwise. 
Changing  the  quality  of  the  judgment  from  negative  to  affirmative,  it 
becomes : 

Some  x  is  not-y ;  Some  men  are  (not- wise)  unwise. 

Praxis. — State  what  is  implied  in  the  following  propositions  by  the 
various  forms  of  implication  just  explained : 

1.  Napoleon  was  an  ambitious  conqueror.  2.  The  diligent  student 
will  become  wise.  3.  Wellington  was  the  soldier  of  duty.  4.  John 
Howard  was  philanthropic.  5.  Greece  is  a  name  of  glory.  6.  War 
is  productive  of  evil.  7.  The  peacemakers  are  blessed.  8.  Cold  kills 
animals. 

Section  III,— Development  of  Inferred  Judgments, 
An  inferred  judgment,  according  to  Davis,  is  "  one  that 
only  virtually  or  potentially  exists  in  the  given  judgment, 
and  is  derived  from  it."  Its  statement  contains  "something 
new,  there  is  a  step  forward,  a  progress  of  thought.  In  the 
inferred  judgment  there  is  always  either  a  different  subject, 
or  a  different  predicate,  from  that  of  the  premise,  and  per- 
haps both." 

The  so-called  inferred  judgments  may  be  reached  from 
11* 


126  PRACTICAL    LOGIC. 

other  judgments  either  by  Addition,  Disjunction,  Conver- 
sion, or  Opposition.  Of  these  forms  the  last  two  are  the 
most  important. 

Topic  First. — Inferred  Judgments  by  Additions. 

Determinants  may  be  added  to  both  terms  of  a  judgment  which  is 
thereby  rendered  more  definite,  e.  g.,  "  A  negro  is  a  fellow-creature ; 
therefore,  a  suffering  negro  is  a  suffering  fellow-creature."  The  orig- 
inal terms  of  the  judgment  may  themselves  be  made  determinants  or 
marks  of  new  conceptions  introduced  into  the  judgment,  e.  g.,  "  Oxy- 
gen is  an  element ;  therefore,  the  decomposition  of  oxygen  is  the  de- 
composition of  an  element."  On  the  same  principles  two  judgments 
may  be  amalgamated ;  as,  "  Honesty  deserves  reward,  and  a  negro  is 
a  fellow-creature ;  therefore,  a  negro  who  shows  honesty  is  a  fellow- 
creature  deserving  of  reward."  Care  must  be  taken  in  all  these  forms 
of  addition  to  keep  the  distribution  of  the  terms  unchanged. 

Topic  Second. — Inferred  Judgments  by  Disjunction. 

Since  the  members  of  a  disjunctive  judgment  are.  'mutually  exclusive, 
we  may  infer  from  the  disjunctive,  "  The  teeth  are  either  incisor, 
canine,  bicuspid,  or  molar  teeth,"  the  judgment,  "  The  molar  teeth  are 
neither  incisor,  canine,  nor  bicuspid."  As  the  dividing  members  in  a 
disjunctive  judgment  exhaust  the  whole  subject  divided,  we  may  infer 
that  the  part  of  the  whole  not  contained  in  one  member  must  be  in 
some  other.  Hence  from  the  judgment  just  given  come  such  inferred 
judgments  as,  "  All  teeth  which  are  not  molar  are  either  canine,  inci- 
sor, or  bicuspid  teeth." 

Topic  Third. — Inferred  Judgments  by  Conversion. 

Illative  Conversion  of  judgments  is  such  a  transposition 
of  the  subject  and  predicate  of  a  judgment  that  the  con- 
verse or  transposed  form  is  a  legitimate  inference  from  the 
convertend  or  original  judgment.  Three  general  Rules  must 
be  observed  in  conversion  : 

Rule  1st.  Before  conversion  reduce  the  proposition  to  the 
strict  logical  form,  in  which  subject,  copula,  and  predicate 
distinctly  appear. 

Rule  2d.  No  term  not  distributed  in  the  convertend  must 
be  distributed  in  the  converse.  We  may  infer  from  all  to 


THE    UNFOLDING    OF   JUDGMENTS.         127 

all,  from  all  to  some,  and  from  some  to  some,  but  not  from 
some  to  all. 

Rule  3d,  The  transfer  of  the  terms  should  be  total.  In 
other  words,  the  whole  naked  subject  (i.  e.,  the  subject 
without  its  sign  of  quantity,  every,  all,  some,  etc.)  must  be 
transferred  to  the  predicate,  and  the  whole  naked  predicate 
must  be  transferred  to  the  subject. 

Confining  attention  mainly  to  the  four  attributive  judgments,  A,  E, 
I,  0, — since  these  are  all  the  forms  of  which  any  special  use  is  ordina- 
rily made  in  compendiums  of  Logic, —  it  will  be  seen  that  there  are 
three  principal  forms  of  conversion. 

First,  Simple  Conversion  when  neither  the  quantity  nor  the  quality 
is  changed ; 

Second,  Conversion  by  Limitation  when  the  quantity  is  changed. 

Third,  Conversion  by  Negation  or  Contraposition,  when  the  qual- 
ity is  changed. 

1.  Simple  Conversion  is  where  the  terms  can  be  trans- 
posed without  change  of  either  quantity  or  quality.     This 
can,  of  course,  occur  only  when  both  subject  and  predicate 
are  distributed,  as  in  E,  and  where  both  are  undistributed, 
as  in  I, 

(1.)  Let  E,  "No  one  without  a  love  of  beauty  can  be  an  eminent 
artist,"  be  given  for  conversion.  The  Rules  should  be  applied  in  order. 
By  Rule  1st,  the  proposition  becomes,  "  Every  one  without  a  love  of 
beauty  is  not  any  one  who  can  be  an  eminent  artist."  By  Rule  2d 
and  Rule  3d,  the  converse  becomes,  "  Any  one  who  can  be  an  eminent 
artist  is  not  any  one  without  a  love  of  beauty."  The  converse  is 
still  E. 

(2.)  Let  I,  "  Some  good  men  are  bad  poets,"  be  given.  The  propo- 
sition is  already  in  strict  logical  form.  By  Rules  2d  and  3d  the  con- 
verse becomes,  "  Some  bad  poets  are  good  men."  The  converse  is 
still  I. 

(3.)  Substitutive  and  equivalentjudgments,  TJ  and  Y,  are,  of  course, 
converted  by  simple  transposition  of  tbe  terms.  "  All  bodies  are  ex- 
tended substances  "  becomes,  "  All  extended  substances  are  bodies." 

2.  Conversion  by  limitation  (per  accidens)  takes  place 


128  PRACTICAL    LOO  1C. 

where  it  is  necessary,  in  order  to  an  illative  transposition, 
that  the  quantity  of  the  proposition  should  be  changed 
from  universal  to  particular,  while  the  quality  remains 
unchanged.  This  will,  of  course,  occur  where  the  subject 
is  distributed  and  the  predicate  undistributed,  i.  e.,  in  A. 
As  some  may  be  inferred  from  all,  E  may  also  be  converted 
by  limitation. 

(1.)  Let  A,  "All  poets  are  men,"  be  given  for  conversion.  It  is 
already  in  strict  logical  form.  In  order  to  conform  to  Rule  2d,  the 
predicate  must  be  limited  to  "  some  men."  By  Rule  3d  the  converse 
becomes,  "  Some  men  are  poets  ;  "  or,  "  Some  men  are  all  the  poets." 
The  converse  of  A  is  I. 

(2.)  Let  E,  "  No  men  are  perfect,"  be  given  for  conversion  by  limi- 
tation. Completing  the  form,  limiting  the  quantity  of  the  predicate, 
and  then  making  a  total  transfer  of  the  terms,  the  converse  becomes, 
"  Some  perfect  things  are  not  men."  The  converse  is  0.  By  simple 
conversion  it  would  be  E. 

3.  Conversion  by  Negation  or  Contraposition  takes  place 
where  it  is  necessary  in  order  to  illative  transposition,  that 
the  quality  of  the  judgment  should  be  changed,  while  the 
quantity  remains  unchanged.  This  occurs  in  0. 

Let  0,  "  Some  quadrupeds  are  not  horses,"  be  given  for  conversion. 
If  converted  simply,  it  would  be,  "  Some  horses  are  not  quadrupeds," 
which  is  absurd.  This  result  is  avoided  by  obverting,  or  infinitating 
the  proposition,  and  then  converting  simply.  Infinitating  the  predicate, 
the  proposition  becomes,  "  Some  quadrupeds  are  (things)  not-horses  ;  " 
and  by  conversion,  "  Some  things  not-  horses  are  quadrupeds."  Thus 
the  converse  of  0  is  I. 

Topic  Fourth. — Inferred  Judgments  by  Opposition. 

Opposition  is  the  name  given  to  the  differences  in  quan- 
tity or  quality,  or  both,  between  judgments  having  the 
same  naked  subject  and  predicate.  Legitimate  inferences 
follow  from  opposition. 

Between  the  judgments,  A,  E,  I,  0,  to  which  attention  is 
here  chiefly  confinecj,  there  are  four  kinds  of  opposition, 


THE    UNFOLDING    OF  JUDGMENTS.         129 

which  are  exhibited  by  the  following  diagram,  called  the 
Square  of  Opposition. 

All  men  are  true,      A Contrary E  No  men  are  true. 


(Subalternans) 


(Subalternans) 


Some  men  are  true,    •    .-*"                          *'•     •  Some  men  are  not  true. 
(Subalternate)          I Subcontrary 0    (Subalternate) 

1.  Contradictory  Opposition,  which  is  the  only  perfect 
form,  exists  between  the  propositions  A  and  0,  E  and  I, 

which  differ  both  in  quantity  and  quality.  By  the  principles 
of  Contradiction  and  of  Excluded  Middle,  of  two  contra- 
dictory propositions  both  cannot  be  true  and  both  cannot 
be  false. 

Rule. — From  the  truth  of  either  of  two  contradictories 
the  falsity  of  the  opposite  follows;  and  from  the  falsity  of 
either  the  truth  of  the  opposite  follows. 

If  A,  "All  men  are  true,"  be  sublated  (denied)  then  we  can  posit 
(affirm)  0,  "  Some  men  are  not  true."  If  it  be  not  true  that  "  All 
men  are  true,"  then  it  is  certain  that,  (at  least)  "Some  men  are 
not  true."  If  0,  "  Some  men  are  not  true,"  be  denied,  then  A,  "  All 
men  are  true,"  may  be  affirmed ;  but  if  the  former  be  affirmed,  the 
latter  may  be  denied. 

Contradictory  opposition  is  of  special  service  in  indirect  proof. 
Instead  of  showing  an  opponent's  arguments  false  and  his  position, 
therefore,  unsustained,  it  is  often  better  to  prove  the  truth  of  the  con- 
tradictory and  then  infer  the  falsity  of  his  position.  E.  g.,  if  one 
affirms  that  "  All  scientists  are  extreme  evolutionists,"  which  is  A, 
the  best  way  to  meet  it  is  by  establishing  the  contradictory  0,  "  Some 
scientists  are  not  extreme  evolutionists  ;  "  or,  "  Some  one  scientist,  as 
Prof.  Tait,  is  not  an  extreme  evolutionist."  If  this  be  established  the 
necessary  inference  is  that  A  is  false.  The  form  of  indirect  proof 
known  as  reductio  ad  absurdum,  largely  used  in  geometrical  demon- 
strations, instead  of  demonstrating  a  proposition  directly,  demonstrates 

I 


130  PRACTICAL    LOGIC. 

that  its  contradictory  is  absurd,  and  thence  immediately  infers  the 
truth  of  the  proposition. 

2.  Contrary  Opposition  is  between  the  universal  proposi- 
tions A  and  E,  which  differ  in  quality  only. 

Rule. — From  the  truth  of  a  judgment  the  falsity  of  its 
contrary  opposite  follows ;  from  its  falsity  nothing  follows. 

Both  A  and  E  cannot  be  true.  From  the  truth  of  A  the  falsity  of 
E  follows,  and  vice  versa.  E.  g.,  if  A,  "  All  men  have  conscience,"  be 
true,  then  E,  "  No  man  has  a  conscience,"  is  false ;  and  if  the  latter  be 
true  then  the  former  is  false.  From  the  falsity  of  one  contrary  nothing 
follows  with  regard  to  the  other.  If  it  be  false  that,  "  All  men  are 
poets,"  it  does  not  follow  that,  "  No  men  are  poets."  But  both  may 
be  false.  E.  g.,  the  propositions,  A,  "All  men  are  poets,"  and  E,  "No 
men  are  poets,"  are  both  false,  since  the  truth  lies  between  the  two 
and  is  expressed  in  I,  "  Some  men  are  poets."  In  individual  proposi- 
tions, as,  "Shakespeare  was  a  poet,"  the  opposition  appears  as  the  sim- 
ple negative,  "  Shakespeare  was  not  a  poet." 

3.  Subcontrary  Opposition  is  between  the  particular  prop- 
ositions I  and  0,  which  differ  in  quality  only. 

Rule. — If  one  sub-contrary  be  true,  nothing  follows  in 
regard  to  the  other ;  but  if  one  be  false,  then  the  other  must 
be  true. 

For  example,  if  I,  "Some  wars  are  evil,"  be  true,  it  does  not  follow 
from  this  that  0,  "  Some  wars  are  not  evil,"  is  true.  But  if  I,  "  Some 
wars  are  evil,"  be  false,  then  "  Some  wars  are  not  evil,"  must  be  true. 

4.  Subalternate  Opposition  is  between  the  propositions 
A  and  I,  E  and  0,  differing  in  quantity  only. 

Rule. — If  the  universal,  A  or  E,  be  true,  the  particular 
I  or  0,  must  be  true ;  and  if  the  particular  I  or  0,  be  false, 
then  the  universal,  A  or  0,  must  be  false. 

If  A,  "  All  men  are  liars,"  is  tr.ue,  then  I,  "Some  men  are  liars,"  is 
also  manifestly  true.  If  I,  "  Some  men  are  perfect,"  is  false,  then  A, 
"  All  men  are  perfect,"  is  false. 

The  results  may  be  summed  up  as  follows : 


<D 


THE  UNFOLDING    OF  JUDGMENTS.        131 


Contradictories.      Contraries.  Subalterns. 

^H    i    If  A  is  true, O  is  false,.... E  false, I  true. 

g    )  If  E     "      I      "      ,....A    "    , O    "  . 

If  A  is  false 0  is  true, E  undetermined,...!  undetermined. 

If  E      "      I      "      ...... A  "  ,...0 

Contradictories.     Subcontraries.         Subalterns. 

If  I  is  true, E  is  false 0  undetermined, ...A  undetermined. 

If  O     "     A      "      ,....!  "  ,...E 

If  I  is  false, E  is  true,....0  true, A  false. 

IfO      "      A      "     ' I     "    , E     "    . 

Praxis. — Apply  exhaustively  the  principles  of  implication  and  al&o 
the  principles  of  immediate  inference  in  its  four  kinds,  to  the  follow- 
ing judgments,  giving  the  quantity  and  quality  of  the  judgments: 

1.  All  the  righteous  are  happy.  2.  No  human  virtues  are  perfect. 
3.  Some  possible  cases  are  probable.  4.  The  just  are  (all)  the  holy. 
5.  Some  men  are  all  the  poets.  6.  All  the  insincere  are  dishonest. 
7.  No  unjust  act  is  unpunished.  8.  Some  unfair  acts  are  unknown. 
9.  The  unlawful  is  the  (only)  inexpedient.  10.  No  brutes  are  re- 
sponsible. 11.  Heaven  from  all  creatures  hides  the  book  of  fate.  12. 
Fair  promises  are  not  often  to  be  trusted. 


SUMMARY    OF    RESULTS. 

THE  aim  of  the  Logic  of  Judgment  is  to  train  to  the 
best  thinking  and  fullest  appreciation  of  thought  in  the 
second  form.  The  perfection  of  thinking  in  judgment  de- 
pends upon  the  certainty  of  the  connection  of  the  subject 
and  predicate.  This  gives  rise  to  what  is  called  the  Modal- 
ity of  Judgments. 

1.  By  the  degree  of  certainty  of  the  predication  to  the 
mind  of  the  thinker  or  others,  all  judgments  have  been 
divided  into  Demonstrative,  Assertory,  and  Problematic. 

(1.)  A  demonstrative  or  apodictic  judgment  is  one  that  is  certain  to 
him  who  holds  it,  and  that  may  be  made  certain  to  all  sane  minds  suf- 


132  PRACTICAL   LOGIC. 

ficiently  intelligent  to  understand  the  signification  of  the  judgment 
itself  and  its  evidence.  All  analytic  judgments  are  demonstrative,  or 
are  certain  to  him  who  holds  them,  and  may  be  made  certain  to  all 
other  sane  minds  of  sufficient  intelligence  to  understand  the  signifi- 
cance of  the  terms.  All  intuitive  judgments  are  also  demonstrative,  or 
have  both  subjective  and  objective  certainty.  These  include  the  truths 
of  Mathematics,  the  fundamental  principles  of  Logic,  the  axioms  of 
Ethics  and  Metaphysics.  All  judgments  reached  by  immediate  infer- 
ence from  these  are  also  demonstratively  certain. 

(2.)  An  assertory  judgment  is  one  that  announces  what  is  known 
as  actual.  It  is  certain  only  to  him  who  holds  it,  but  not  capable  of 
being  made  certain  to  others  of  different  moral  disposition.  "  It  com- 
mends itself  to  our  moral  nature,  and  in  so  far  as  other  men  are  of  the 
same  disposition,  they  will  accept  it  likewise."  This  holds  especially 
of  higher  moral  and  religious  truths.  Moral  and  religious  deterio- 
ration prevents  their  acceptance. 

(3.)  "  A  problematic  judgment  is  one  that  is  neither  held  with  entire 
certainty  by  the  thinking  subject,  nor  can  we  show  that  it  truly  rep- 
resents the  object  about  which  we  judge.  It  is  a  mere  opinion" 
Problematic  judgments  constitute  one  of  the  necessary  stages  in  the 
progress  towards  truth.  "  Great  discoveries  are  problems  at  first  .  .  . 
Whenever  we  judge  about  variable  things,  as  the  future  actions  of 
men,  the  best  course  of  conduct  for  ourselves  under  doubtful  circum- 
stances, historical  facts  about  which  there  is  conflicting  testimony,  we 
can  but  form  a  problematical  judgment,  and  must  admit  the  possibility 
of  error  at  the  moment  of  making  our  decision." 

2.  A  simpler  division  of  j  udgments,  by  the  degree  of  cer- 
tainty in  the  mind  of  the  thinker,  is  into  Certain,  Probable, 
and  Doubtful. 

(1.)  A  certain  judgment  is  one  in  which  the  knowledge  that  the 
connection  between  the  subject  and  predicate  corresponds  to  the  reality 
is  absolute  and  unquestionable.  All  analytic  judgments,  all  intuitive 
judgments,  all  immediate  inferences  from  certain  judgments,  all  strict 
deductions  from  certain  or  necessary  premises  may  become  certain  to 
the  thinker. 

(2.)  A  probable  judgment  is  one  in  which  the  knowledge  that  the 
connection  between  the  subject  and  predicate  corresponds  with  the  re- 
ality is  not  absolute  and  unquestionable.  The  boundary  line  between 
the  probable  and  doubtful  is  not  always  clearly  marked,  since,  in  com- 


THE    UNFOLDING    OF   JUDGMENTS         133 

mon  language,  the  degrees  of  probability  may  reach  all  the  way  from 
the  nearest  approach  to  certainty  that  a  judgment  is  true,  down  to 
the  nearest  approach  to  certainty  that  it  is  not  true,  i.  e.,  from  the 
nearest  possible  to  absolute  certainty,  to  the  nearest  possible  to  abso- 
lute uncertainty ;  while  the  degrees  of  doubtfulness  may  have  the 
same  wide  scope.  It  may  be  said,  however,  in  general,  that  a  strictly 
probable  judgment  is  one  which  has  the  balance  of  proof  in  its  favor, 
and  that  a  doubtful  judgment  is  one  which  has  the  balance  of  proof 
against  it.  As  has  already  been  seen,  man  receives  most  of  the  knowl- 
edge used  in  the  conduct  of  life,  in  such  a  way  that  it  is  not  certain, 
but  at  best  only  more  or  less  probable.  All  the  acquired  perceptions 
of  the  senses  and  consciousness  are  mixed  with  inferences,  and,  there- 
fore, only  probable ;  while  only  the  original  or  intuitive  perceptions 
are  certain.  The  conclusions  of  finite  reason,  especially  by  the  induc- 
tive processes,  are  liable  to  error,  and,  therefore,  cannot  rise  to  certainty. 
The  judgments  based  on  testimony  and  authority  can  at  best  reach 
only  a  high  degreee  of  probability.  A  judgment  may  be  possible  when 
it  is  not  probable.  "  A  thing  is  said  to  be  possible  when,  though  not 
actually  in  existence,  all  the  conditions  necessary  for  realizing  its  ex- 
istence are  given."  It  is  possible,  for  example,  that  aerial  transporta- 
tion may  some  day  take  the  place  of  transportation  by  steamer  and 
railway,  but  not  perhaps  probable. 

The  aim  of  the  Practical  Logic  of  Judgment  should  be 
to  train  the  thinker  to  skill  in  distinguishing  clearly  be- 
tween the  certain,  the  probable,  and  the  doubtful ;  and  in 
arriving  at  sound  judgments,  on  the  basis  either  of  cer- 
tainty or  of  probability,  by  which  to  govern  the  entire  con- 
duct of  human  life. 
12 


PART  III. 


THE  LOGIC  OF  REASONING  OR  THE  SYLLOGISM. 


THE  aim  of  the  Logic  of  Reasoning  is  to  train  the  mind 
to  skill  in  dealing  with  the  third  Form  of  Thought. 

Definition. — Reasoning  is  that  form  of  thought  in  which 
we  compare  various  judgments  and,  on  the  ground  of  some 
medium  or  cause,  reach  other  judgments  as  inferences  or 
conclusions  from  them.  Reasoning  may,  therefore,  be  used 
as  synonymous  with  Mediate  Inference.  The  product  of 
reasoning,  as  embodied  in  language,  is  usually  known  as 
the  Syllogism. 

Note.— Mediate  inference  is  inference  by  a  medium,  or  middle  notion  or  term. 
It  is  thus  distinguished  from  immediate  inference  which,  as  has  been  seen  (p. 
121),  does  not  make  use  of  any  such  third  or  middle  term.  The  middle  term 
is  used  where  we  cannot  compare  two  things  directly.  We  cannot  compare 
two  lots  directly  by  placing  one  upon  the  other,  but  we  can  measure  them  both 
with  a  surveyor's  chain,  or  other  common  measure,  and  thus  ascertain  their 
relative  dimensions.  So  when  two  notions  or  terms  cannot  be  directly  compared 
and  connected  they  may  be  indirectly  by  the  use  of  a  third  notion  or  term. 
We  may,  e.  g.,  wish  to  connect "  John  Baptist"  and  "  priest "  in  the  judgment, 
"  John  Baptist  was  a  priest."  Having  no  direct  statement  to  that  effect  in  the 
Bible,  we  must  reach  the  conclusion  by  reasoning  from  the  fact  that  the  sons 
of  priests  were  also  priests.  The  process  of  thought  is  stated  as  follows : 

Analytic  Form.  Synthetic  Form. 

f  John  Baptist  was  a  priest ;  f  The  son  of  a  priest  was  a  priest ; 

•j  For  he  was  the  son  of  a  priest ;  4  John  Baptist  was  the  son  of  a  priest ; 

(  And  the  son  of  a  priest  was  a  priest.    (. .'.  John  Baptist  was  a  priest. 

Both  terms  are  connected  with  a  third  term,  "son  of  a  priest,"  and  thus 
connected  with  each  other. 

134 


THE  FORMATION   OF   REASONING.        135 

The  most  helpful  logical  presentation  of  Reasoning  must  treat  of 
both  the  formation  of  reasonings  or  syllogisms  and  the  unfolding  of 
syllogisms.  The  present  subject  will,  therefore,  embrace  two  Chapters. 


CHAPTER    I. 

THE  FORMATION  OF  REASONING  OR 
MEDIATE  INFERENCE. 

THE  formation  of  thought  as  reasoning  must  manifestly 
be  placed  at  the  foundation  in  all  training  to  thought  in  its 
third  form.  It  will  be  necessary  to  consider,  in  successive 
Sections,  the  nature  of  reasoning  or  mediate  inference  in 
general,  and  the  fundamental  forms  of  reasoning1, — deduc- 
tion and  induction.  The  process  and  the  products  will  be 
considered  under  each  of  the  forms  of  reasoning. 

Note.— Much  of  the  modern  depreciation  of  Logic,  and  especially  of  the 
Logic  of  the  Syllogism,  is  doubtless  due  to  the  fact  that  the  Science  has  been 
confined  largely  to  the  mechanical  testing  of  barren  forms.  If  this  be  all  there 
is  in  the  Logic  of  Reasoning,  it  would  have  to  be  admitted  that  it  is  not  a  very 
valuable  means  of  knowledge ;  the  old  objection  would  hold,  that  "  the  prem- 
ises, so  far  from  being  able  to  establish  the  truth  of  the  conclusion,  presup- 
pose it."  Take  in  illustration  a  syllogism  commonly  given:  "All  Cretans  are 
liars ;  this  man  is  a  Cretan ;  therefore  he  is  a  liar."  How  do  we  know  all  before 
we  know  each  f  How  do  we  know  all  before  the  character  of  this  particular 
Cretan  is  decided?  That  is,  until  we  are  certain  that  this  particular  Cretan  is 
a  liar,  we  cannot  be  certain  that  all  Cretans  are  liars. 

The  all-important  thing  in  reasoning  is  the  finding  of  middle  terms 
or  connecting  links  of  argumentation ;  and  even  the  testing  of  the 
various  products  of  reasoning  cannot  proceed  intelligently  without 
some  skill  in  finding  these  connecting  links. 

Section  I,— The  Process  of  Reasoning  or  Mediate  Inference 

in  General, 
Topic  First. — The  Forms  of  Reasoning. 

All  reasoning  necessarily  proceeds  from  general  princi- 
ples to  particulars  or  individuals,  or  from  facts  or  particu- 
lars to  general  principles.  Mediate  Inference  is,  therefore, 


136  PRACTICAL    LOO  1C. 

divided  into  two  chief  kinds :  Deduction,  or  Specialization, 
or  Syllogism  in  the  stricter  sense  ;  and  Induction,  or  Gen- 
eralization, or  Syllogism  in  the  looser  sense. 

Syllogism  in  the  stricter  sense  in  its  chief  forms  is  inference  from 
the  general  to  the  particular  or  individual,  and  in  all  its  forms  infer- 
ence proceeding  from  the  general.  Induction  is  inference  proceeding 
from  the  individual  or  particular  to  the  general.  Inference  by  anal- 
ogy, which  proceeds  from  the  individual  or  particular  to  a  co-ordinate 
individual  or  particular,  is  a  third  form  distinct  from  both,  though 
able  to  be  reduced  to  a  combination  of  the  other  two.  See  Ueberweg's 
Logic,  p.  333. 

Deduction  has  also  been  called  "  the  inference  of  subordination,"  or 
"  inference  by  analysis  of  notions ;  "  induction,  "  the  inference  of  su- 
perordination ;  "  analogy,  "  the  inference  of  co-ordination." 

The  difference  between  deduction  and  induction  may  be  illustrated 
by  the  methods  of  proving  that  the  interior  of  the  earth  is  in  a  molten 
condition.  From  the  volcanic  phenomena,  i.  e.,  from  the  facts  that 
the  earth  is  in  a  molten  condition  under  Mount  Vesuvius,  Mount  Hecla, 
Mauna  Loa,  etc.,  it  is  inferred  inductively  that  the  whole  interior  is  in 
such  condition.  From  the  process  of  the  earth's  formation  by  the  con- 
densation of  intensely  heated  material  (an  origin  probable  on  astro- 
nomical grounds),  it  is  inferred  deductively  or  syllogistically  that  the 
interior  is  in  a  molten  condition.  The  one  process  starts  from  facts ; 
the  other  from  a  general  principle.  They  are  usually  thrown  into 
syllogistic  form,  as  follows : 

Inductive  Process.  Deductive  Process. 


The  interior  of  the  earth  is 
molten ; 

For,  it  is  molten  under  Vesu- 
vius, etc. ; 

And  Vesuvius,  etc.,  fairly  rep- 
resents the  whole. 


The   interior  of   the    earth  is 

molten ; 
For  the  solar  system  was  formed 

by  condensation ; 
And  the  earth  is  a  part  of  the 

solar  system. 


The  nature  of  analogy,  as  made  up  of  induction  and  deduction,  may 
be  shown  from  the  following  example  :  "  The  Earth,  a  planet  revolv- 
ing in  an  orbit  round  our  sun,  turning  on  its  axis,  having  an  atmo- 
sphere, change  of  seasons,  etc.,  supports  organic  life ;  Mars  is  a  planet 
revolving  in  an  orbit  round  our  sun,  turning  on  its  own  axis,  having 
an  atmosphere,  change  of  seasons,  etc. ;  hence  Mars  also  will  probably 
support  organic  life."  It  will  be  seen  by  examination  that  this  consists 


THE   FORMATION    OF  REASONING.        137 

of  an  apparent  induction  and  a  deduction  combined.     This  may  be 
exhibited,  in  full,  as  follows : 

[~     The  Earth  supports  organic  life ; 

The  Earth  is  a  planet  revolving,  etc.,  and  fairly  represents  that 

class  of  planets ; 

.*.  All  planets  revolving,  etc.,  probably  support  organic  life ; 
^  |~~     Mars  is  a  planet  so  revolving,  etc. ; 
P  [_.'.  Mars  probably  supports  organic  life. 

According  to  the  common  view  both  deduction  and  in- 
duction may  be  embodied  in  syllogistic  form  (as  in  the 
examples  given).  The  elements  of  the  reasoning,  as  em- 
bodied in  the  syllogism,  need,  therefore,  to  be  considered. 
As  the  validity  of  the  reasoning  depends,  however,  not 
upon  the  syllogistic  forms,  but  upon  the  connecting  link  of 
thought  embodied  in  the  middle  term,  the  subject  of  find- 
ing middle  terms  needs  to  be  specially  considered. 

Note.— The  question  whether  all  reasoning  can  be  reduced  to  the  syllogism 
is  one  into  which  we  have  not  space  to  enter.  Nor  is  there  need  to  discuss  it 
here,  since  it  is  freely  admitted  that  the  validity  of  the  reasoning  depends  upon 
the  connecting  links  of  thought  and  not  upon  the  form;  and  that  the  syllogism  is 
of  no  special  value  in  the  formation  of  processes  of  reasoning,  but  only  in 
formulating  and  testing  them  after  they  are  formed. 

Topic  Second. — The  Elements  of  Reasoning. 

The  elements  of  reasoning  are  ascertained  by  analyzing 
the  process  as  embodied  in  the  Syllogism.  The  syllogism 
is  composed  of  three  terms  and  three  propositions ;  and 
underlying  the  form,  as  the  real  basis  of  thought,  is  some 
mediating  notion  or  cause. 

I.  The  Terms  and  Propositions. 

The  terms  or  notions  in  the  syllogism  are  distinguished 
as  the  major  term,  the  minor  term,  and  the  middle  term. 
The  propositions  in  the  usual  form  of  statement  are  the 
major  premise  and  the  minor  premise,  constituting  the  ante- 
cedent or  proof,  and  the  conclusion  or  consequent. 

The  conclusion  is  the  judgment  to  be  proved.     In  the  formal  syllo- 
gism it  is  placed  last.     Its  subject,  represented  by  S,  is  the  minor  term ; 
12* 


138  PRACTICAL    LOGIC. 

its  predicate,  represented  by  P,  is  the  major  term.  The  middle  term, 
represented  by  M,  is  that  with  which  the  major  and  minor  are  com- 
pared in  the  premises. 

The  major  premise  is  the  judgment  in  which  the  major  term  or 
predicate  of  the  conclusion  is  compared  with  the  middle. 

The  minor  premise  is  the  judgment  in  which  the  minor  term  is 
compared  with  the  middle. 

This  may  be  illustrated  in  concrete  form  and  in  formula,  as  follows : 

All  conquerors  (M)  are  tyrants  (P)  ;~|  f  M  is  P ;  Major  Premise. 
Napoleon  (S)  was  a  conqueror  (M) ;  <  S  is  M  ;  Minor  Premise. 
Napoleon  (S)  was  a  tyrant  (P).  J  l.'.S  is  P.  Conclusion. 


The  conclusion  is  reached  by  comparison  of  both  its  terms 
with  the  third  or  middle  term,  "  conqueror." 

II.  The  Middle  Term  or  Connecting  Link. 

The  middle  notion  or  term  (originally  called  the  argu- 
ment) always  represents  the  link  of  thought  by  which  the 
two  terms  of  the  conclusion  are  brought  together  and  the 
judgment  proved.  It  furnishes  the  sufficient  reason  for 
connecting  the  major  and  minor  terms.  Reasoning  is  prop- 
erly, therefore,  finding  the  sufficient  reason— in  case  of  in- 
duction the  cause — for  the  connection  of  the  terms  in  the 
conclusion. 

Various  maxims  have  been  formulated  to  express  the  connection 
embodied  or  implied  in  the  middle  term.  The  principal  are  those  of 
Aristotle  and  Kant,  which  apply  respectively  to  propositions  of  extent 
and  content,  or  to  propositions  made  up  of  class  terms  and  those 
made  up  of  attribute  terms.  The  axiom  of  Sufficient  Reason,  or  of 
Reason  and  Consequent,  is,  however,  the  best  and  most  complete 
expression  of  this  connection. 

The  so-called  dictum  of  Aristotle  places  the  relation  of  genus  and  species  at 
the  foundation  of  reasoning.  Whatever  can  be  predicated  affirmatively  or 
negatively  of  any  genus  or  class  distributed  can  be  predicated  likewise  of  all 
or  any  of  the  species  or  individuals  included  under  it.  If  it  can  be  affirmed 
of  the  genus  man,  that  it  is  included  in  the  higher  genus  person,  then  it  can 
be  affirmed  of  the  species  slaves,  included  under  man,  that  it  is  included  under 
person.  Or  if  it  can  be  affirmed  of  the  genus  man,  that  it  is  excluded  from  the 
genus  brute,  then  the  same  can  be  affirmed  of  the  species  poets,  included  under 
the  genus,  man. 


THE   FORMATION    OF  REASONING.          139 

The  formula  of  Kant  places  the  relation  of  a  complex  property  to  its  compo- 
nents at  the  foundation  of  reasoning.  Whatever  is  a  component  of  a  complex 
property  of  a  tiling  is  a  property  of  the  thing  itself.  The  mark  brave,  which 
is  a  component  of  the  complex  mark  conqueror,  is  also  a  mark  of  Caesar, 
the  object  to  which  the  complex  conqueror  applies. 

Others  make  the  relation  at  the  basis  of  reasoning  that  of  whole  and  part.  A 
part  of  a  part  is  also  a  part  of  the  whole. 

The  real  connecting  principle  or  basis  in  reasoning,  i.  e.,  the  real 
sufficient  reason,  is,  perhaps,  best  expressed  by  the  relation  of  reason 
and  consequent,  which,  as  has  already  been  seen  (p.  20),  embraces 
whole  and  part,  cause  and  effect,  substance  and  attribute,  genus  and 
species,  etc.  Any  form  of  reason  and  consequent  may  be  at  the  basis 
of  deduction;  while  the  basis  of  induction  is  the  strictly  causal  rela- 
tion only. 

Topic  Third.— Finding  and  Verifying  Arguments  or  Mid- 
dle Terms. 

From  what  has  been  thus  far  considered,  it  is  obvious 
that  reasoning  essentially  consists  in  finding  and  verifying 
arguments,  or  middle  terms  and  causes,  under  the  principle 
of  Sufficient  Reason  or  Reason  and  Consequent.  This  pro- 
cess differs  in  deduction  and  induction,  inasmuch  as  these 
forms  of  reasoning  differ. 

Section  II. —  Deductive  Keasoning. 

Topic  First.  —  Process  of  Finding  and  Verifying  the 
Argument  in  Deduction. 

Three  things  are  essential  in  deduction:  first,  finding  the 
proper  middle  term  ;  second,  verifying  the  premises  formed 
by  the  aid  of  it ;  third,  testing  the  conclusion. 

I.  Finding  the  Middle  Term. 

The  first  question  is,  By  what  middle  term  can  the  two 
given  terms  be  bound  together  or  disjoined  in  the  conclu- 
sion ?  The  following  Rules  will  guide  the  thinker  in  his 
quest : 

Rule  1st. — Examine  carefully,  by  the  principles  laid  down  in  the 
Logic  of  Conception,  the  two  terms  to  ba  connected  or  disjoined,  m 


140  PRACTICAL    LOGIC. 

order  to  ascertain  which  of  the  relations  under  reason  and  consequent 
is  applicable  to  them. 

Rule  2d. — Seek  the  proper  mediating  whole,  concept  proper,  class, 
or  cause,  as  the  case  may  require. 

Rule  3d. — Bring  the  middle  term  thus  found  into  proper  connection 
with  the  other  terms  and  these  with  each  other  in  syllogistic  statement. 

The  application  of  these  Rules  may  be  illustrated  by  examples. 
Thus,  in  seeking  a  middle  term  to  prove  that  "The  Persians  worship  a 
thing  insensible"  we  find,  by  the  first  Rule,  that  this  term  must  be  an 
individual  under  the  genus,  "  things  insensible."  By  the  second  Rule, 
"the  sun"  furnishes  such  an  individual.  By  the  third  Rule,  these 
are  brought  together  in  syllogistic  statement,  in  the  order  of  proof,  as 
follows : 

The  Persians  worship  a  thing  insensible ;     Question. 
For  the  Persians  worship  the  sun ;  )  jx.    / 

And  the  sun  is  a  thing  insensible.    I 

Again,  in  finding  a  middle  term  to  prove  that  "Judas  was  not  a  true 
apostle,"  we  find,  by  the  first  Rule,  that  the  major  term,  "  true  apos- 
tle," is  a  genus  or  class  term.  By  the  second  Rule,  "thief"  furnishes 
a  "genus"  excluded  from  the  genus,  "true  apostle."  By  the  third 
Rule,  this  takes  shape  as  follows : 

Judas  was  not  a  true  apostle  ;          Question. 
For  Judas  was  a  thief ;  \  P     f 

And  no  thief  was  a  true  apostle.  ) 

Once  more,  in  proving  that  "Plato  is  mortal,"  we  find,  by  the  first 
Rule,  that  the  major  term,  "  mortal,"  is  a  concept  or  attribute  term. 
By  the  second  Rule,  we  find  that  the  complex  concept,  "  man,"  in- 
cludes "mortal"  as  a  component  property;  and,  therefore,  since  the 
mark  of  a  mark  is  a  mark  of  the  thing  itself,  "  mortal "  is  a  mark  of 
"  Plato."  By  the  third  Rule,  this  gives,  stated  in  twofold  syllogistic 
form: 

f  Plato  is  mortal ;  Question.      r     Man  is  mortal ;   1  p      /• 

<  For  Plato  is  man  ;     1  <j      Plato  is  man ;      ) 

I  And  man  is  mortal.  /  1  .'.  Plato  is  mortal.      Conclusion. 

II.  Verifying  the  Premises. 

When  the  middle  term  has  thus  been  found  and  con- 
nected with  the  major  and  minor  terms,  the  question  arises, 
Are  these  premises  true  ?  Hence  the  following  Rule  : 


THE   FORMATION    OF   REASONING.         141 

Rule  4th. — Test  the  premises  by  the  principles  already  presented 
for  the  verification  of  judgments  (p.  98),  in  order  to  be  sure  that  only 
correct  judgments  have  been  grasped. 

It  is  all  important  that  correct  judgments  should  be  grasped  and 
placed  at  the  foundation  as  premises,  since  otherwise  any  inferences 
from  them  would  be  logically  worthless.  The  sources  of  the  judgments 
made  use  of  in  deduction  are  the  following :  intuition ;  thought  proper 
inductive  and  deductive ;  and  testimony  and  authority.  The  prem- 
ises must  be  tested  by  the  principles  by  which  judgments  from  these 
various  sources  are  proved. 

III.  Testing  the  Conclusion, 

When  the  premises  have  been  found  to  be  true  or  prob- 
able, the  question  arises,  Does  the  conclusion  follow  from 
the  premises  f  Hence  the  following  Kule  : 

Rule  5th. — Test  the  whole  process  by  the  principles  of  analysis  pre- 
sented in  the  Logic  of  Conception,  and  by  the  laws  which  govern  the 
Syllogism  as  presented  in  the  next  Chapter  under  the  Unfolding  of 
Reasoning. 

Partial  understanding  of  the  terms  may  lead  to  false  conclusions. 
This  may  be  prevented  by  a  careful  study  and  analysis  of  the  con- 
cepts and  terms  involved,  by  means  of  Partition,  Division,  and  Defi- 
nition. False  conclusions  may  also  be  drawn  from  correct  premises. 
This  may  be  prevented  by  the  careful  use  of  the  formal  rules  of  the 
Syllogism. 

In  all  deductive  reasoning,  it  should  be  remembered, 
that  the  conclusion  can  never  be  any  more  certain  than  the 
premises.  Forgetfulness  of  this  is  the  source  of  many  and 
great  errors  in  both  Science  and  Philosophy. 

Topic  Second,— Products  of  Deductive  Reasoning. 

The  product  of  deduction  is  the  Syllogism  proper  in  its 
various  forms.  Syllogisms  are  divided,  by  the  form  of  the 
judgments  embodied  in  them,  into  categorical  and  hypo- 
thetical. Categorical  syllogisms  are  either  simple  or  com- 
bined,— simple  when  they  contain  but  one  argument  with 
its  major  and  minor  premises  expressed  or  understood  and 
its  conclusion ;  combined  when  more  than  one  process  of 


142  PRACTICAL    LOGIC. 

argument  is  involved.     The  former  may  be  called  the  mono- 
syllogism  ;  the  latter  the  polysyllogism. 

I.  Categorical  Syllogisms. 

A  categorical  syllogism  is  one  in  which  the  judgments 
are  categorical  (p.  117). 

1.  The  mono  syllogism  may  be  in  its  statement  either 
complete  or  incomplete. 

The  complete  form  is  the  ordinary  form  in  which  both  the  premises 
and  the  conclusion  are  expressed.     The  incomplete  form  or  the  enthy- 
meme  (Greek,  meaning  in  the  mind)  is  that  form  in  which  one  premise 
is  unexpressed,  or  left  to  be  supplied  by  the  mind.     Thus : 
"  Alexander  the  Great  was  brave ; 
For  he  was  a  conqueror." 

In  this  case  the  major  premise,  "All  conquerors  are  brave,"  is  omitted. 
The  minor  premise  may  also  be  omitted.     Thus : 
"  Conquerors  are  brave ; 
Therefore  Alexander  the  Great  was  brave." 

Note. — The  enthymeme  is  the  usual  form  in  ordinary  speech.  The  premise 
left  unexpressed  is  easily  supplied  in  completing  the  syllogistic  statement. 
It  will  also  be  seen  that  in  common  speech  there  are  to  be  found  many  abridged 
and  disguised  forms  of  argument.  For  example :  "  Hard  study  strengthens  the 
mind,  but  wearies  the  flesh ;  so  that  what  wearies,  strengthens ; "  "  Theft  is  a 
crime ;  yet  some  kinds  were  legal  in  Sparta."  In  such  cases  the  first  step  is  to 
reduce  the  argument  to  the  normal  form. 

2.  The  polysyllogism  includes  the  various  forms  in  which 
separate  syllogisms  are  combined  into  wholes  of  connected 
reasoning.     Syllogisms  may  be  attached,  as  prosyllogisms, 
to  premises  to  prove  them,  or,  as  episyllogisms,  to  conclu- 
sions, making  the  conclusions  premises  for  reaching  further 
conclusions.     In  the  former  case  the  prosyllogisms  are  sub- 
ordinate to  a  principal  syllogism,  and  the  whole  constituted 
is,  therefore,  a  complex  syllogism,  which  may  be  known  as 
the  epichirema;  in  the  latter  case  the  episyllogisms  are 
co-ordinate  with  that  to  which  they  are  attached,  and  the 
whole  is,  therefore,  a  compound  syllogism. 

(1.)    The  Complex  Syllogism,  or  Epichirema,  or  reason-rendering 


THE   FORMATION    OF   REASONING.         143 

syllogism,  is  either  manifest  (i.  e.,  having  all  the  parts  fully  expressed), 
or  occult  (i.  e.,  having  some  of  the  parts  suppressed).  Both  the  mani- 
fest and  occult  forms  may  be  "  either  single  or  double,  according  as 
one  or  both  of  the  premises  are  furnished  with  an  auxiliary  reason." 

The  single  epichirema,  in  both  its  occult  and  manifest  forms,  may  be  illus- 
trated by  the  following  example : 

Main  Syllogism.   Occult  Prosyllogism.        Expanded  Prosy llogism. 
Vice  is  odious ;  f     Whatever  enslaves  is  a  vice  ; 

Avarice  is  a  vice,  for  [it  enslaves ;]     J      Avarice  enslaves ; 
.-.Avarice  is  odious.  (  .'.Avarice  is  a  vice. 

Omitting  the  expanded  prosyllogism,  we  have  the  ordinary  single  epichi- 
rema in  its  occult  form ;  omitting  the  occult  prosyllogism,  we  have  the  same 
in  its  manifest  form. 

The  double  epichirema,  in  both  its  occult  and  manifest  forms,  may  be  illus- 
trated by  the  following  example : 

Main  Syllogism.        Occult  Prosyllogisms.         Expanded  Prosyllogisms. 
Man  has  a  spirit ;  for  [he  is  rational ;  =]    r     Every  rational  being  has  a 

J          spirit; 

j      Man  is  a  rational  being ; 
V. .'.  Man  has  a  spirit. 

Man  has  a  body ;  for  [he  fills  space ;  =1    f      Whatever  fills  space  has  a 

J         body; 
j      Man  fills  space ; 
Something  that  has  a  spirit  has  body.       (.  /.  Man  has  a  body. 

Omitting  the  expanded  prosyllogisms,  we  have  the  double  epichi- 
rema in  its  occult  form;  omitting  the  occult  prosyllogisms,  we  have 
the  same  in  its  manifest  form. 

(2.)  The  compound  syllogism,  made  up  of  successive  co-ordinate 
syllogisms,  includes  the  double  syllogism,  in  which  the  episyllogism 
is  attached  to  the  conclusion  of  a  syllogism,  making  that  conclusion  a 
premise  for  reaching  a  new  conclusion  ;  and  the  chain  syllogism, 
which  is  made  up  of  successive  co-ordinate  syllogisms.  In  both  these 
forms  it  may  be  either  manifest  or  occult. 

The  double  syllogism  of  the  compound  form  does  not  need  to  be 
further  subdivided.  The  chain  syllogism  in  its  occult  form  is  usually 
known  as  the  sorites  (Greek,  meaning  a  heap}.  The  successive  syllo- 
gisms in  it  are  all  equally  abridged. 


Both  the  manifest  and  occult  forms  may  be  illustrated  by  the  following  ex- 
amples, in  which  the  occult  forms  are  contractions  of  the  manifest  forms : 

Double  Syllogism,  Manifest  Form. 
Useful  studies  ought  to  be  pursued ; 
1st,  \      Logic  is  a  useful  study ; 

Logic  ought  to  be  pursued. 


I 


144  PRACTICAL    LOGIC. 

{A  course  which  omits  what  ought  to  be  studied  is  deficient ; 
A  course  which  omits  Logic  omits  what  ought  to  be  studied ; 
.*.  A  course  which  omits  Logic  is  deficient. 

Double  Syllogism.  Occult  Form. 

Useful  studies  ought  to  be  pursued ;  ) 
Logic  is  a  useful  study ; 

.•  Logic  ought  to  be  pursued ;  J  Syllogism. 

Hence  an  educational  course          l 
which  omits  Logic  is  deficient.    /  EPlsy"°glsm- 

Chain  Syllogism,  Occult,  Sorites.  Chain  Syllogism,  Manifest. 

Bucephalus  is  a  horse ;  I.   f       Bucephalus  is  a  horse ; 

A  horse  is  a  quadruped; 
/.  Bucephalus  is  a  quadruped. 

A  horse  is  a  quadruped;          II.   f      Bucephalus  is  a  quadruped ; 

A  quadruped  is  an  animal ; 
Bucephalus  is  an  animal. 

A  quadruped  is  an  animal ;   III.    f      Bucephalus  is  an  animal ; 
An  animal  is  a  substance ;  An  animal  is  a  substance ; 

Bucephalus  is  a  substance.  [  v  Bucephalus  is  a  substance. 

The  sorites  proper  is  of  two  kinds, — the  progressive  or  Aristotelian, 
in  which  the  argument  descends  from  whole  to  part ;  and  the  regres- 
sive or  Goclenian,  in  which  the  argument  ascends  from  part  to  whole, 
as  in  the  following  examples : 

Regressive  Sorites.  Progressive  Sorites. 

Bucephalus  is  a  horse ;  An  animal  is  a  substance ; 

A  horse  is  a  quadruped ;  A  quadruped  is  an  animal ; 

A  quadruped  is  an  animal ;  A  horse  is  a  quadruped ; 

An  animal  is  a  substance ;  Bucephalus  is  a  horse ; 

.•.  Bucephalus  is  a  substance.  /.  Bucephalus  is  a  substance. 

The  sorites  can  thus  readily  be  expanded  into  a  manifest  compound 
syllogism.  It  consists  of  "as  many  simple  syllogisms  as  there  are 
middle  terms  between  the  subject  and  predicate  of  the  conclusion,  i.  e.t 
intermediate  wholes  and  parts  between  the  greatest  whole  and  the 
smallest  part,  which  the  reasoning  connects."  In  the  example  given, — 
taking  the  progressive  form, — the  greatest  whole  and  smallest  part  are 
substance  and  Bucephalus;  the  middle  terms  are  horse,  quadruped, 
animal.  This  gives  three  simple  syllogisms,  by  using  successively 
these  middle  terms. 

II.  Hypothetical  Syllogisms. 

The  hypothetical  syllogism  is  that  form  of  syllogism  in 
which  the  reasoning  turns  upon  some  hypothetical  judg- 
ment (p.  117)  embodied  in  the  major  premise.  Hypotheti- 


THE   FORMATION    OF   REASONING.         145 

cal  syllogisms,  whether  monosyllogisms  or  polysyllogisms, 
are,  therefore,  primarily  divided  into  conditional  or  con- 
junctive and  disjunctive.  These,  as  in  the  case  of  cate- 
goricals,  may  be  either  manifest  or  occult. 

1.  A  hypothetical  monosyllogism  is  one  which  contains 
but  one  argument,  with  its  major  and  minor  premises  ex- 
pressed or  understood,  and  its  conclusion.     The  suppressed 
or  disguised  premise  gives  the  hypothetical  enthymeme 
which  is  the  most  common  form  in  ordinary  speech.     Both 
manifest  and  occult  hypothetical  arguments  may  be  either 
conditional  or  disjunctive. 

(1.)  A  conditional,  or  conjunctive  hypothetical  syllogism  is  one  in 

which  the  reasoning  turns  upon  a  conditional  or  conjunctive  judg- 
ment embodied  in  the  major  premise.  This  may  be  illustrated  in  both 
its  manifest  and  occult  forms  by  the  following  example : 

Manifest  Form.  Enthymeme. 

If  rains  are  plenty,  the  crops  will  be  f  If  rains  are  plenty,  crops  will  be 
plenty ;  J     plenty ; 

Rains  are  plenty :  1 

/.  Crops  will  be  plenty.  (.  So  crops  will  be  plenty. 

(2.)  A  disjunctive  hypothetical  syllogism  is  one  in  which  the  rea- 
soning turns  upon  a  disjunctive  judgment  embodied  in  the  major 
premise.  This  may  be  illustrated  by  the  following  example : 

Manifest  Form.  Enthymeme. 

{Man  is  either  an  automaton  or  free ;  f  Man  is  either  an  automaton  or  free; 
He  is  a  free  being;  J 

.-.  He  is  not  an  automaton.  [  And  so  he  is  assuredly  free. 

2.  The  hypothetical  polysyllogism  includes  the  various 
forms  in  which  hypothetical  arguments  may  be  brought  to- 
gether into  wholes  of  connected  reasoning.     These  wholes 
may  arise  from  combining  hypothetical  and  disjunctives 
in  the  premises,  or  by  combining  entire  arguments.     The 
former  gives  rise  to  dilemmatic  syllogisms;   the  latter  to 
compound  hypothetical  syllogisms,  including  the  double 
form  and  the  sorites. 

(1.)  A  dilemmatic  syllogism  is  one  having  a  dilemmatic  judgment 
(p.  118)  for  its  major  premise,  with  a  minor  premise  so  affirming  or 
13  K 


146  PRACTICAL    LOGIC. 

denying  some  member  or  members  of  the  major  as  to  lay  the  founda- 
tion for  an  inference.  The  forms  depend  upon  the  various  combina- 
tions in  the  major  premise.  The  combinations  are  as  follows  : 

1st.  A  single  conditional  antecedent  with  a  disjunctive  consequent, 

as  in  the  example : 

If  the  Senator  aspires  to  a  place,  he  will  either  rule  or  ruin : 
The  Senator  aspires  to  the  place  of  President : 
.*.  He  will  either  rule  or  ruin. 
Or,  If  A  is  B,  either  C  is  D  or  E  is  F ; 

But  A  is  B,  ...  /.  either  C  is  D  or  E  is  F. 

2d.  A  plurality  of  conditional  antecedents  all  having  one  common 
consequent,  as  in  the  example : 

"If  things  are  what  we  can  help,  we  ought  not  to  fret  about  them;  and  if 
they  are  what  we  cannot  help,  we  ought  not  to  fret  about  them ; 

But  all  things  are  either  what  we  can  or  cannot  help ;, 
/.  They  are  what  we  ought  not  to  fret  about." 

Or,  If  A  is  B,  X  is  Y,  and  if  C  is  D,  X  is  Y; 
But  either  A  is  B  or  C  is  D ; ... .-.  X  is  Y. 

This  form  is  what  has  been  known  as  the  dilemma  in  the  strict  sense, 
or  the  horned  syllogism.  It  is  so  called  because  it  confronts  an  oppo- 
nent with  two  assumptions,  on  which  it  tosses  him  as  on  horns  from 
one  to  the  other,  each  being  equally  fatal  to  him. 

3d.  A  plurality  of  conditional  antecedents  each  with  its  own  con- 
sequent, as  in  the  example : 

f  If  men  are  virtuous  they  are  wise,  Or,  If  A  is  B,  C  is  D,     ) 

I  And  if  they  are  vicious  they  are  unwise ;      And  if  E  is  F,  G  is  H ;  / 

But  they  are  either  virtuous  or  vicious ;         But  either  A  is  B,  or  E  is  F ; 
.-.  They  are  either  wise  or  unwise.  .'.  Either  C  is  D,  or  G  is  H. 

(2.)  The  compound  hypothetical  syllogism  includes  the  double  form, 

in  which  the  latter  of  two  syllogisms  is  abridged,  and  appears  as  an 
episyllogism;  and  the  hypothetical  sorites,  in  which  the  successive 
syllogisms  are  all  equally  abridged.  These  may  be  illustrated  by  ex- 
amples : 

Double  Form. 

{If  the  people  are  industrious,  wealth  increases; 
They  are  industrious ;  Episyllogism. 

.'.  Wealth  is  increasing  (and  hence  the  nation  mil  become  power/til). 

Hypothetical  Sorites. 

If  Gladstone  is  virtuous,  he  is  brave ;  Or,  If  A  is  B,  C  is  D ; 

If  brave,  he  is  magnanimous ;  If  C  is  D,  E  is  F ; 

If  magnanimous,  he  will  relieve  the  Irish  ten- 1          T  „  _  .   _,  _  .   _ 
ants;  /          IfEisF.GisH; 

But  Le  is  virtuous,  and  /.  will  relieve  the  Irish  )          _,  . 
tenants.  f  1S  B>  '*' 


THE   FORMATION    OF  REASONING.          147 

Praxis. — Find  middle  terms  for  the  following  conclusions,  according 
to  the  Rules  given ;  verify  the  premises  and  test  the  conclusion ;  and 
mark  by  the  appropriate  vowels  the  quantity  and  quality  of  all  the 
judgments:  1.  Jupiter  is  a  planet.  2.  Education  is  valuable.  3. 
Religion  is  indispensable.  4.  The  crocodile  is  a  reptile.  5.  Few 
patriots  have  been  disinterested.  6.  No  brutes  are  responsible.  7. 
Perseverance  is  a  condition  of  success.  8.  A  sensualist  is  not  truly 
free.  9.  The  elk  is  ruminant.  10.  Good  logicians  are  not  true  poets. 
11.  The  immoral  man  is  not  happy.  12.  The  inactive  man  cannot  be 
happy.  13.  Astrology  is  not  a  science.  14.  Astronomy  is  a  science. 

Give  a  complete  outline  of  the  kinds  of  Syllogisms,  as  presented  in 
the  preceding  Section,  and  then  construct  one  or  more  original  syllo- 
gisms illustrating  each  of  the  kinds. 

Section  III,— Inductive  Seasoning, 

Topic  First.— Process  of  Finding  and  Verifying  the  Cause 
in  Induction. 

Two  things  are  essential  in  induction :  first,  fixing  upon 
some  assumed  cause  which  works  in  the  facts  from  which 
the  inference  is  sought,  and  which  furnishes  the  basis  for 
a  working  hypothesis ;  second,  testing  and  verifying  this 
hypothesis. 

Note.— Ueberweg  has  said  truly:  "  Hypotheses  are  necessary  in  all  sciences 
if  the  knowledge  of  causes  is  to  be  reached.  Causes  as  such  are  not  accessible 
to  observation,  and,  therefore,  at  first  can  be  thought  only  under  the  form  of 
hypotheses,  until,  with  the  advance  of  the  sciences,  the  previously  problem- 
atic suppositions  pass  over  into  knowledge  apodictically  certain.  .  .  Scientific 
hypotheses  .  .  .  are  the  results  of  regular  reflection  on  experience,  and,  as 
premises  in  tentative  deductions,  form  the  necessary  preliminaries  to  ade- 
quate knowledge." 

I.  Finding  the  Working  Hypothesis. 

In  finding  the  cause  in  induction,  the  first  question  to  be 
asked  is,  What  working  hypotheses,  in  themselves  possible, 
can  be  formed,  which  agree  with  the  facts  of  experience,  so 
that  the  phenomena  may  all  be  taken  into  account  and  ex- 
plained ? 

Induction  derives  its  data  from  experience.  Experience  is  the  ex- 
amination which  is  necessary  to  furnish  us  the  facts  from  which  to 


148  PRACTICAL   LOGIC 

make  inferences.     Such  experience  is  obtained  either  by  observation  or 
by  experiment. 

Observation  is  the  act  of  the  mind  in  seizing  upon  facts  as  they  are  sponta- 
neously presented  in  nature.  Its  nature  and  methods  have  already  been 
unfolded  (p.  26).  Experiment  is  the  process  of  voluntarily  "  putting  in  action 
causes  and  agents  over  which  we  have  control,  and  purposely  varying  their 
combinations  and  noticing  what  effects  take  place."  It  vastly  multiplies  the 
possibilities  of  observation,  and  is  thus  of  the  greatest  importance  to  science. 
The  data  drawn  from  experience  for  use  in  induction  consist  of  facts  or  phe- 
nomena. A  phenomenon  means  literally  "  that  which  appears  to,  or  is  known 
directly  by,  the  senses,"  and  then  "  that  which  is  known  as  a  fact  to  the  mind." 
The  word,  therefore,  includes  all  facts  whether  made  known  by  the  senses  or 
consciousness.  The  word  fact  is  substantially  its  equivalent  in  usage.  It  sig- 
nifies literally  "something  done,"  and  maybe  defined  to  be  anything  that 
exists  or  happens,  whether  in  the  world  of  matter  or  of  mind. 

Equally  important  with  the  data  of  induction  is  the  correct  logical 
method  of  dealing  with  the  facts.  This  Bacon  sought  to  furnish  in 
his  Novum  Organum  or  New  Instrument.  Its  aim  is  to  direct  the  mind 
in  seizing  upon  the  facts  in  any  given  region,  constructing  hypotheses 
for  their  explanation,  and,  through  the  verification  of  these,  reaching 
perfected  theories  or  general  truths. 

"  The  correct  construction  of  hypotheses,"  says  Ueberweg,  "  is  a 
life  and  death  question  with  Philosophy ;  for  it  is  the  science  of  the 
principles  which  underlie  all  the  sciences,  and  requires  more  than 
any  other  to  pass  beyond  mere  experience,  and  to  bring  together  by 
comparison  very  different  departments  of  knowledge."  Hence  the 
importance  of  correct  Rules  carefully  applied. 

Bale  1st. — Observe,  analyze,  and  classify  the  facts  to  be  generalized 
and  explained,  in  order  to  ascertain  their  reality  and  their  various 
elements  and  relations. 

This  Rule  guards  against  two  common  sources  of  error  in  induction.  The 
first  is  that  of  assuming  what  is  not  fact  to  be  fact.  This  is  illustrated  by  the 
problem  presented  by  Charles  II.  to  the  Royal  Society :  "  Why  does  a  live  fish 
in  water  increase  the  weight  while  a  dead  fish  does  not?"  The  answer  to  the 
question,  "  Is  it  a  fact  ?"  would  have  saved  the  time  spent  in  endeavoring  to 
solve  the  imaginary  problem.  The  second  is  the  error  from  getting  only  a 
partial  view  of  the  facts  or  from  failure  to  get  them  in  their  relations.  This  is 
illustrated  in  Stahl's  method  of  accounting  for  combustion,  by  the  extrication 
of  a  substance  supposed  to  be  contained  in  all  combustible  matter,  called 
phlogiston,  which  went  up  in  the  flame.  Combustion  results  in  the  visible 
residue  of  ashes  and  the  invisible  phlogiston  which  passes  off.  The  error  was 
in  the  non-observation  of  an  important  part  of  the  actual  residue, — the  gas- 
eous products  of  combustion.  When  these  were  at  last  taken  into  account,  it 
was  found  that  the  gases  with  the  ashes  weighed  much  more  than  the  sub- 
stance burned,  so  that  there  was  no  room  for  phlogiston.  See  Mill's  Logic, 
Book  V.,  Ch.  iv. 


THE   FORMATION    OF  REASONING.          149 

"Rule  2d. — Correctly  interpret  the  facts,  i.  e.,  seek  to  find  the  appro- 
priate cause  for  the  facts  and  basis  for  the  generalization. 

By  cause  in  induction  is  meant  "  operating  power,"  or,  more 
strictly,  "  power  which  in  operating  originates  new  forms  of  being." 
It  is  anything  which  has  efficiency  and  exerts  it  in  producing  change, 
and  hence  is  often  called  efficient  cause.  It  should  be  carefully  dis- 
tinguished from  law,  which  has  no  efficiency,  but  is  merely  an  expres- 
sion of  an  established  sequence  of  facts,  or  of  the  regular  order  in 
which  a  cause  operates.  A  condition  is  "  that  which  is  prerequisite 
in  order  that  something  may  be,  and  especially  in  order  that  a  cause 
may  operate."  It  is  "  prior  to  the  production  of  an  effect;  but  it  does 
not  produce  it.  It  is  fire  that  burns ;  but,  before  it  burns,  it  is  a 
condition  that  there  be  an  approximation  of  the  fire  to  the  fuel,  or 
the  matter  that  is  burned.  .  .  The  cause  of  burning  is  the  element  of 
fire,  fuel  is  the  con-cause,  and  the  condition  is  the  approximation  of 
the  one  to  the  other." 

The  cause  may  be  sought,  first,  in  some  known,  or.  secondly,  in  some  un- 
known, force  or  forces.  The  search  in  the  former  case  has  to  do  with  some 
real  cause  and  is  guided  by  the  so-called  Methods  of  Induction,  and  in  the 
latter  case  must  be  reached  by  inductive  assumption  or  assumption  of  strictly 
hypothetical  cause.  In  the  former  case  the  results  tend  to  take  shape  in  contri- 
butions to  exact  science ;  in  the  latter  they  belong  to  the  region  of  scientific 
question  or  metaphysical  speculation.  The  quarrels  of  scientists  and  theolo- 
gians very  often  arise  from  confounding  the  two. 

(1.)  Inductions  of  Real  Cause. — The  Canons  of  the  In- 
ductive Method  used  in  the  search  for  the  real  cause  for 
any  phenomenon,  whether  that  cause  is  simple  or  complex, 
may  have  reference  either  to  the  preliminary  consideration 
of  the  happening  or  not  happening  of  the  event,  the  cause  of 
which  is  sought;  or  to  the  more  advanced  problem  of  meas- 
uring the  exact  quantity  of  an  effect,  if  it  be  capable  of  being 
more  or  less,  and  connecting  it  with  the  quantity  of  the  cause. 
To  the  first  stage  belong  the  methods  of  agreement  and  of 
difference ;  to  the  second,  the  methods  of  concomitant  vari- 
ation and  of  residues. 

A.  What  can  be  learned  of  the  real  cause  of  an  event 
from  the  happening  or  not  happening  of  that  event  ? 

The  Method  of  Agreement  is  applied  in  case  of  the  uniform  hap- 
pening of  an  event.     This  gives  rise  to — 
13* 


150  PRACTICAL    LOGIC. 

Canon  First. — If  in  all  observed  cases  of  an  effect  or  phenomenon 
one  condition  is  uniformly  present,  that  is  probably  the  cause,  or  in- 
cludes the  cause,  of  the  phenomenon  or  effect.  In  other  words,  "  the 
sole  invariable  antecedent  of  a  phenomenon  is  probably  its  cause." 

"  To  apply  this  method  we  must  collect  as  many  instances  of  the  phenom- 
enon as  possible,  and  compare  together  their  antecedents.  Among  these  the 
causes  will  lie,  but  if  we  notice  that  certain  antecedents  are  present  or  absent 
without  appearing  to  affect  the  result,  we  conclude  that  they  cannot  be  neces- 
sary antecedents." 

The  method  of  agreement  is  subject  to  a  serious  difficulty.  An  antecedent 
may  not  be  a  cause.  Night  or  the  cock-crowing  or  the  rising  of  some  diligent 
workman  may  uniformly  precede  the  coming  of  the  day  without  being  the 
cause  of  it.  Hence  the  necessity  for  tests  by  which  to  distinguish  between 
simple  antecedent  and  real  cause. 

The  Method  of  Difference  is  applied  in  case  of  the  uniform  happen- 
ing of  an  event  in  the  case  of  the  presence  of  some  condition,  and  the 
uniform  failure  of  it  in  case  of  the  absence  of  that  condition.  This 
gives  rise  to 

Canon  Second. — If,  in  all  instances  in  which  a  phenomenon  does 
occur,  one  single  condition  is  present,  which  is  uniformly  absent 
whenever  such  phenomenon  does  not  occur,  this  constantly  present  or 
absent  condition  is  presumed  to  be  the  cause  of  the  phenomenon. 

Thus  we  can  clearly  prove  that  friction  is  one  cause  of  heat,  because  when" 
two  sticks  are  rubbed  together  they  become  heated ;  when  not  rubbed  they  do 
not  become  heated.  Sir  Humphrey  Davy  showed  that  even  two  pieces  of  ice 
when  rubbed  together  in  a  vacuum  produce  heat,  as  shown  by  their  melting, 
and  thus  completely  demonstrated  that  the  friction  is  the  source  and  cause 
of  the  heat.  We  prove  that  air  is  the  cause  of  sound  being  communicated  to 
our  ears,  by  striking  a  bell  in  the  receiver  of  an  air-pump,  as  Hawksbee 
first  did  in  1705,  and  then  observing  that  when  the  receiver  is  full  of  air  we 
hear  the  bell ;  when  it  contains  little  or  no  air  we  do  not  hear  the  bell. 

B.  What  can  be  learned  of  the  Real  Cause  of  an  event 
from  the  varying  degree  or  quantity  of  an  event  ? 

"  Every  science  and  every  question  in  science  is,"  as  Jevons  has 
said,  "  first,  a  matter  of  fact  only,  then  a  matter  of  quantity,  and  by 
degrees  becomes  more  and  more  precisely  quantitative.  Thirty  years 
ago  most  of  the  phenomena  of  electricity  and  electro-magnetism  were 
known  merely  as  facts ;  now  they  can  be  for  the  most  part  exactly 
measured  and  calculated. 

"  There  is  in  fact  a  natural  course  of  progress  through  which  we 
proceed  in  every  such  inquiry,  as  may  be  stated  in  the  following  se- 
ries of  questions. 


THE   FORMATION    OF   REASONING.          151 

1.  Does  the  antecedent  invariably  produce  an  effect? 

2.  In  what  direction  is  that  effect? 

3.  How  much  is  that  effect  in  proportion  to  the  cause  ? 

4.  Is  it  uniformly  in  that  proportion  ? 

5.  If  not,  according  to  what  law  does  it  vary  ?  " 

The  Method  of  Concomitant  Variations  is  applied,  after  phenomena 
begin  to  be  measured,  in  cases  where  there  is  an  increase  or  decrease  of 
an  event  with  a  corresponding  increase  or  decrease  of  the  condition 
which,  by  the  other  methods,  has  been  assumed  to  be  the  cause.  This 
gives  rise  to 

Canon  Third. — Increase  or  diminution  of  t'he  effect,  accompanied  by 
the  increased  or  diminished  intensity  of  the  assumed  cause,  in  cases 
which  admit  of  increase  and  diminution,  increases  the  assurance  of 
the  causal  relation. 

By  the  method  of  difference  it  may  be  shown  that  air  is  the  cause  of  the 
transmission  of  sound,  by  striking  a  bell  in  the  air  and  in  a  vacuum.  Instead 
of  this,  the  method  of  concomitant  variations  may  be  applied,  by  striking  a 
bell  in  the  receiver  of  an  air-pump  with  a  very  little  air,  and  then  increasing 
and  decreasing  the  density  of  the  air.  The  sound,  which  is  very  faint  with  a 
little  air,  grows  fainter  and  disappears  as  the  air  is  exhausted,  and  becomes 
louder  and  fuller  as  air  is  added. 

This  method  is  made  use  of  in  seeking  causes  for  events  which  go  through  pe- 
riodic changes,  alternately  increasing  and  decreasing.  It  leads  us  to  search  for  a 
cause  which  undergoes  like  periodic  changes.  The  tides  are  thus  proved  to 
be  due  to  the  combined  attraction  of  the  moon  and  sun,  since  the  periods  of 
high  and  low,  spring  and  neap,  tides  succeed  each  other  in  intervals  corre- 
sponding to  the  apparent  revolutions  of  those  bodies  round  the  earth. 

But  all  these  methods  are  subject  to  difficulty  from  the  fact  that 
causes  are  usually  complex,  or,  in  other  words,  that  there  is  usually 
a  plurality  of  causes  co-operating  in  the  production  of  any  given 
effect.  This  gives  rise  to 

The  Method  of  Residues  or  of  Eesidual  Variations. — When  there 
are  several  causes  each  producing  a  part  of  the  effect,  we  desire  to 
know  how  much  is  due  to  each  cause.  This  leads  to 

Canon  Fourth. — Subtract  from  any  phenomenon  such  part  as  is 
known  by  previous  inductions  to  be  the  effect  of  certain  of  the  causes, 
and  the  residue  of  the  phenomenon  is  the  effect  of  the  remaining  causes. 

This  is  illustrated  by  the  method  of  ascertaining  the  exact  weight  of  a  load 
of  hay  or  any  other  commodity  in  a  cart,  by  weighing  the  cart  and  load  to- 
gether, and  then  subtracting  the  tare  or  weight  of  the  cart  alone,  previously 
ascertained.  Almost  all  the  remarkable  modern  predictions  in  astronomy 
have  been  made  by  the  use  of  the  method  of  residues.  Thus,  after  the  effects 
of  all  known  attractions  were  calculated  in  the  case  of  Uranus,  it  was  still 


152  PRACTICAL   LOGIC. 

found  that  the  planet  was  sometimes  before  and  sometimes  behind  its  calcu- 
lated place.  This  residual  effect  pointed  to  the  existence  of  some  cause  of 
attraction  not  then  known,  and  the  exact  place  and  size  of  the  disturbing 
body  was  calculated  and  the  planet  Neptune  discovered. 

"  The  motions  of  several  comets  have  in  this  way  been  calculated,  but  it 
is  observed  that  they  return  each  time  a  little  later  than  they  ought.  This  re- 
tardation points  to  the  existence  of  some  obstructive  power  in  the  space 
passed  through,  the  nature  of  which  is  not  yet  understood." 

When  the  same  phenomenon  may  be  the  effect  of  any  one  of  various 
causes,  there  arises  the  necessity  for  excluding  all  the  causes  but  that 
which  really  operates  in  the  given  case.  Ordinarily  this  is  not  a 
difficult  matter.  It  requires,  however,  that  the  attendant  circum- 
stances should  be  carefully  noted  and  understood.  A  room  may  be 
heated  by  the  August  sun,  or  by  a  fire  in  furnace  or  grate  or  stove,  or 
by  any  one  of  various  other  causes.  Which  is  the  operating  cause 
may  be  ascertained  by  the  proper  inspection,  the  real  cause  being 
thus  found  and  all  others  excluded. 

(2.)  Inductions  of  Hypothetical  Cause, — When  the  cause 
of  any  given  phenomenon  is  unknown  or  beyond  our  reach, 
the  assumption  of  some  hypothetical  cause  becomes  a  ne- 
cessity of  the  human  mind.  Such  cases  are  in  the  region 
of  tentative  science  or  scientific  speculation,  rather  than  in 
that  of  exact  science.  Rule  2d  requires  in  such  cases  that 
the  cause  or  causes  assumed  should  be  appropriate  and  ade- 
quate to  account  for  all  the  facts. 

Eule  3d. — When  the  facts  have  been  sufficiently  investigated  com- 
bine them  all  under  the  cause,  simple  or  complex,  which  seems  best 
suited  to  produce  them,  and  which  is  at  work  in  all  similar  facts. 
This  gives  the  working  hypothesis,  which  must  be  modified  to  suit  the 
further  developments  of  investigation. 

As  the  observation  may  be  more  or  less  complete,  various  working 
hypotheses  may  be  reached  by  the  same  thinker  or  by  different 
thinkers. 

When  the  facts  concerning  the  movements  of  bodies  on  the  earth  and  in  the 
heavens  have  been  to  some  extent  observed,  they  may  be  referred  to  gravity 
as  the  cause.  When  the  investigation  has  been  carried  still  further,  the  work- 
ing hypothesis  of  universal  gravitation,  of  Newton,  may  be  stated  :  "Any  two 
masses  in  the  universe,  whatever  their  material,  attract  each  otlier  by  gravitation  with 
a  force  which  varies  directly  as  the  mass  and  inversely  as  the  square  of  the  dis- 
tance." 


THE    FORMATION    OF  REASONING.         153 

This  is  the  work  of  the  constructive  imagination  or  of 
the  power  of  scientific  construction,  and  must  always  pre- 
cede complete  and  established  scientific  theory. 

II.  Testing  the  Working  Hypothesis. 

Scientific  thinking  requires  that  to  the  most  ingenious 
boldness  in  forming  working  hypotheses  should  be  united 
the  most  cautious  accuracy  in  testing  them  before  their 
acceptance  as  truth.  The  tests  of  hypotheses  are  found  in 
connection  with  the  cause  assumed,  the  facts  to  be  explained, 
or  the  application  of  the  deductive  method. 

"A  riper  inquiry,"  says  Ueberweg,  "  recognizes  that  in  all  problems  where 
we  must  proceed  upon  mere  observation,  and  not  with  mathematical  certainty, 
the  scientific  correctness  of  distinct  hypotheses  must  be  the  first  object  of 
investigation.  An  essential  advance  in  method  in  this  sense  was  made  in 
Astronomy,  when  in  the  Platonic  school,  and  especially  by  Heraclides  of  Pon- 
tus,  the  question  to  be  investigated  was  not  stated  in  this  way :  What  positions 
and  motions  of  the  heavenly  bodies  are  to  be  necessarily  accepted  on  empir- 
ical and  speculative  grounds?  but  in  this :  What  hypotheses  of  regular  motions, 
in  themselves  possible,  can  be  formed  which  agree  with  the  facts  of  observa- 
tion, so  that  the  phenomena  may  be  '  preserved '  ?  " 

Rule  1st. — See  that  the  hypothesis  in  each  case  embodies  a  cause 
or  complex  of  causes  which  is  appropriate,  sufficient,  and,  if  possible, 
known  and  true.  This  is  the  cause  test. 

All  rival  hypotheses  should  be  considered  and  fairly  tested  accord- 
ing to  this  Rule.  The  direction  of  Ueberweg  is  as  follows :  "  Let  all 
the  opposing  fundamental  qpinions  be  brought  under  the  view  of  dif- 
ferent thoroughly  testing  hypotheses,  and  do  not  let  the  one  opinion 
(as  too  often  happens  if  it  is  the  traditional  one)  be  treated  from  outset 
as  correct,  necessary,  sound,  and  rational,  and  those  of  opponents  con- 
sidered to  be  false,  arbitrary,  unsuitable,  or  foolish." 

The  Rule  suggests  various  particulars  to  be  noted  in  settling  the 
claims  of  rival  hypotheses. 

1st.  The  hypothesis  which  is  to  be  of  service  must  embody  a  cause. 

The  hypothesis  of  evolution,  as  stated  by  Spencer,  embodies  no  cause :  "  Evo- 
lution is  a  change  from  an  indefinite,  incoherent  homogeneity  to  a  definite, 
coherent  heterogeneity  through  continuous  differentiations  and  integration." 
"  A  change  "  is  not  a  cause,  but  is  rather  the  very  thing  to  be  explained.  This 
is  true  of  a  vast  region  of  so-called  inductions,  which  are  not  inductions  at  all, 
because  there  is  no  cause  at  the  foundation  of  the  facts.  For  example,  it  might 
readily  be  concluded,  from  the  fact  that  man  and  all  the  animals  with  which 


154  PRACTICAL    LOGIC. 

we  come  in  contact  move  the  lower  jaw  in  masticating  food,  that  all  animals 
do  the  same.  The  fact,  however,  is  that  the  crocodile  moves  the  upper  jaw. 
This  is  mere  generalization,  and  not  induction  in  the  proper  sense. 

2d.  The  hypothesis  is  to  be  preferred  which  embodies  an  appro- 
priate cause. 

The  universe  is  found  by  scientific  investigation  to  be  a  thought-system.  Of 
various  hypotheses  concerning  its  production,— by  chance,  by  self-origination 
through  blind  matter  and  force,  by  an  Intelligent  Author  capable  of  planning 
and  constructing  such  a  thought-system,  etc.,— the  hypothesis  of  an  Intelli- 
gent Author  is  the  only  scientific  one,  since  such  a  cause  is  the  only  appro- 
priate one  for  the  effect. 

3d.  The  hypothesis  is  to  be  preferred  which  embodies  a  known 
cause. 

Induction  assumes  the  simplicity  of  nature.  That  is,  the  Author  of  nature 
works  as  man  would  work,  using  the  simplest  means  to  attain  the  end  in  view, 
never  introducing  a  new  force  where  some  already  existing  force  will  accom- 
plish the  object.  On  this  principle  Newton  extended  the  familiar  action  of 
the  known  force  of  gravity  on  the  earth's  surface  to  the  phenomena  of  the 
heavens. 

4th.  The  hypothesis  is  to  be  preferred  which  embodies  a  true  cause. 

Newton's  view  of  gravitation  made  use  of  a  true  cause,  which  "  had  been 
already  known  as  an  actual  power  in  nature,  in  the  power  of  weight  upon  the 
earth." 

When  no  known  agent  can  be  found,  it  becomes  necessary  to  assume  some 
unknown,  but  appropriate  and  adequate,  cause.  Thus,  the  physicist  in 
accounting  for  the  phenomena  of  light,  electricity,  etc.,  assumes  the  existence 
of  ether,  an  extremely  tenuous  substance,  pervading  all  bodies  and  extending 
through  the  universe,  which  is  the  vibratory  medium  in  the  transmission  of 
all  these  forms  of  energy.  This  is,  of  course,  a  strictly  hypothetical  cause. 
Some  other  hypothesis  may,  at  some  future  time,  take  its  place. 

5th.  The  hypothesis  is  to  be  preferred  which  takes  into  account  the 
complex  nature  of  causes  and  makes  the  right  ones  prominent. 

Almost  universally  in  nature  causes  are  manifold  and  complex,  and  none 
of  the  complex  elements  can  be  overlooked  without  falling  into  error.  For 
example,  about  1854,  some  excavators  broucht  up  some  burnt  brick  and  pot- 
tery from  the  depth  of  60  and  72  feet,  in  the  valley  of  the  Nile.  Assuming 
that  they  were  found  where  they  were  made,  and  that  the  alluvium  had  been 
deposited  upon  them  at  the  rate  at  which  the  Nile  now  makes  its  deposit,  and 
that  this  was  the  only  cause  at  work,  it  was  calculated  mathematically  that  the 
relics  must  be  from  12,000  to  60,000  years  old.  One  causal  element  omitted 
was  the  weight  of  the  brick-bats  in  connection  with  the  fact  (also  causal)  that 
all  the  region  is  a  vast  quagmire  during  the  inundation  which  covers  it  with 
water  during  a  large  part  of  the  year.  Sir  Robert  Stephenson  afterwards 
found  in  the  Delta  near  Damietta,  at  a  far  greater  depth,  a  brick  bearing  the 
stamp  of  Mohammed  AH  (1808).  Some  one  said  satirically  that  the  main  ques- 
tion in  the  first  case  should  have  been  :  How  long  will  it  take  a  brick  to  sink 
72  feet  in  a  quagmire?  But  although  this  might  be  the  main  question,  all 
causes  should  be  given  their  due  weight  in  reaching  the  correct  result. 


THE   FORMATION    OF  REASONING.        155 

Bale  2d. — See  that  the  hypothesis  in  each  case  combines  and  ex- 
plains all  the  facts.  This  is  the  fact  test.  This  embraces  various 
particulars. 

1st.  The  hypothesis  must  embrace  the  facts. 

This  is  the  object  in  forming  hypotheses,  and  forgetfulness  of  it  is  fatal  to 
correct  thinking.  The  question  in  inductive  science  should  not  be,  what  must 
be  ?  but,  what  is  ?  The  old  science,  putting  assumption  and  deduction  in  the 
place  of  induction  from  facts,  taught  that  the  orbits  of  the  heavenly  bodies 
must  be  circular,  because  "  the  circle  is  the  perfect  figure ;"  the  true  science 
teaches  that  the  orbits  of  the  heavenly  bodies  are,  in  fact,  ellipses,  because  this 
alone  agrees  with  the  facts  as  explained  by  the  laws  of  centrifugal  and  cen- 
tripetal force  in  connection  with  gravitation  and  the  motion  of  the  bodies. 

2d.  The  hypothesis  must  explain  all  the  facts.  A  single  fact  clearly 
contradictory  to  any  hypothesis  calls  for  the  modification  or  abandon- 
ment of  the  hypothesis. 

It  is  manifest  that  even  a  single  fact  clearly  contradictory  to  any 
hypothesis  proves  the  hypothesis  untenable,  as  that  single  fact,  though 
there  were  no  other  such  fact,  would  prove  the  principle  embodied  in 
the  hypothesis  not  universal.  The  place  occupied  by  exceptional  facts 
is  thus  seen  to  be  very  important.  As  Jevoiis  has  said,  "  they  are 
commonly  the  points  from  which  we  start  to  explore  new  regions  of 
knowledge."  As  all  exceptions  are  not  equally  fatal  to  the  hypotheses 
to  which  they  appear  to  be  exceptional,  Jevons  (Principles  of  Science, 
pp.  644-672)  has  arranged  them  under  eight  classes : 

(1.)  "  Imaginary,  or  false,  exceptions,  that  is,  facts,  objects,  or  events  which 
are  not  really  what  they  are  supposed  to  be. 

(2.)  "Apparent  but  congruent  exceptions,  which,  though  apparently  in  con- 
flict with  a  law  of  nature,  are  really  in  agreement  with  it. 

(3.)  "  Singular  exceptions,  which  really  agree  with  a  law  of  nature,  but  ex- 
hibit remarkable  and  unique  results  of  it. 

(4.)  "  Divergent  exceptions,  which  really  proceed  from  the  ordinary  action 
of  known  processes  of  nature,  but  which  are  excessive  in  amount  or  monstrous 
in  character. 

(5.)  "  Accidental  exceptions,  arising  from  the  interference  of  some  entirely 
distinct  but  known  law  of  nature.  This  is  the  largest  class  of  exceptions. 

(6.)  "  Novel  and  unexplained  exceptions,  which  lead  to  the  discovery  of  a 
new  series  of  laws  and  phenomena,  modifying  or  disguising  the  effects  of  pre- 
viously known  laws,  without  being  inconsistent  with  them. 

(7.)  "  Limiting  exceptions,  showing  the  falsity  of  a  supposed  law  in  some 
cases  to  which  it  has  been  extended,  but  not  affecting  its  truth  in  other  cases. 

(8.)  "  Contradictory  or  real  exceptions,  which  lead  us  to  the  conclusion  that 
a  supposed  hypothesis  or  theory  is  in  opposition  to  the  phenomena  of  nature, 
and  must  therefore  be  abandoned."  These  exceptions  are  the  most  important 
of  all,  "  since  they  lead  to  the  entire  rejection  of  a  law  or  theory  before  ac- 
cepted." No  law  of  nature  can  fail;  there  are  no  such  things  as  real  excep- 
tions to  real  laws.  Where  contradiction  ex-ists,  it  must  be  in  the  mind  of  the 


156  PRACTICAL    LOGIC. 

experimentalist.  Either  the  law  is  imaginary  or  the  phenomena  which  con- 
flict with  it ;  if,  then,  by  our  senses  we  satisfy  ourselves  of  the  actual  occurrence 
of  the  phenomena,  the  law  must  be  rejected  as  illusory. 

Rule  3d. — Apply  the  principles  of  deduction  to  the  hypothesis,  as- 
certaining what  ought  to  happen  in  any  given  circumstances  if  the 
hypothesis  he  true,  and  test  the  predicted  results  by  observation  and 
experiment.  This  is  the  prediction  test. 

When  any  hypothesis  embodies  a  real  cause,  it  gives  the  thinker  the  power 
of  predicting  by  deduction  the  particular  phenomena  which  come  under  it. 
The  verification  of  such  predictions  is  one  of  the  last  and  highest  tests  of  an 
induction.  "There  is  no  more  convincing  proof  of  the  soundness  of  knowl- 
edge than  that  it  confers  the  gift  of  foresight."  Astronomy  furnished  the 
earliest  development  of  this  power.  Thales,  the  Father  of  Philosophy,  pre- 
dicted the  eclipse  which  suddenly  turned  day  into  night  during  a  battle  be- 
tween the  Medes  and  Lydians.  The  recent  discovery  of  Neptune  is  the  most 
remarkable  instance  of  this  prevision.  The  method  of  prediction  by  deduction 
is  equally  applicable  to  all  the  physical  and  mental  sciences. 

"  As  we  deduce  more  and  more  conclusions  from  any  hypothesis  and  find 
them  verified  by  trial,  the  probability  of  the  theory  increases  in  a  rapid  man- 
ner; but  we  never  escape  the  risk  of  error  altogether.  Absolute  certainty  is 
beyond  the  powers  of  inductive  investigation,  and  the  most  plausible  supposi- 
tion may  ultimately  be  proved  false. 

"Such  is  the  groundwork  of  similarity  in  nature,  that  two  very  different 
conditions  may  often  give  closely  similar  results.  We  sometimes  find  our- 
selves, therefore,  in  possession  of  two  or  more  hypotheses  which  both  agree 
with  so  many  experimental  facts  as  to  have  great  appearance  of  truth.  Under 
such  circumstances  we  have  need  of  some  new  experiment,  which  shall  give 
results  agreeing  with  one  hypothesis  but  not  with  the  other."  This  gives  rise 
to  what  Bacon  called  an  Experimentum  Crucis,  an  "  Experiment  of  the  Fin- 
ger Post."  In  Pascal's  day  his  own  hypothesis,  that  the  mercury  rose  in  the 
tube  because  of  the  pressure  of  the  atmosphere,  had  as  its  rival  the  doctrine, 
that  this  phenomenon  was  due  to  nature's  abhorrence  of  a  vacuum.  His  ex- 
periment of  causing  a  barometer  to  be  carried  to  the  top  of  the  Puy-de-D6me 
was  the  crucial  experiment  which  established  his  own  theory  and  negatived 
the  rival  hypothesis. 

Rule  4th. — Avoid  the  common  error  of  assuming  unverified  hypoth- 
eses, or  such  as  are  based  upon  other  unverified  hypotheses,  as  true. 

The  failure  to  conform  to  this  general  rule  has  been  the  bane  of  sci- 
entific investigation  in  both  its  physical  and  mental  spheres  in  all  ages. 
The  spirit  of  speculation  and  the  determination  to  believe  one's  own 
dreams  to  be  the  reality  have  overborne  the  spirit  of  the  true  philoso- 
pher. "The  philosopher,"  says  Faraday,  "should  be  a  man  willing 
to  listen  to  every  suggestion,  but  determined  to  judge  for  himself.  He 
should  not  be  biased  by  appearances ;  have  no  favorite  hypothesis  ; 
be  of  no  school ;  and  in  doctrine  have  no  master.  He  should  not  be 
a  respecter  of  persons,  but  of  things.  Truth  should  be  his  primary 


THE   FORMATION   OF    REASONING.         157 

object.     If  to  these  qualities  be  added  industry,  he  may  indeed  hope 
to  walk  within  the  veil  of  the  temple  of  nature." 

Topic  Second.  —  Products  of  Inductive  Reasoning. 

The  product  of  induction  is  a  generalization.     The  pro- 
cess may  be  expressed  in  quasi-syllogistic  form,  as  follows  : 

Mars,  Jupiter,  the  Earth  .........  move  in  elliptical  orbits  round  the  sun; 

These  are  (as  good  as—  or  fairly  represent)  all  the  planets  ; 
/.  All  the  planets  move  in  elliptical  orbits  round  the  sun. 

Or  letting  Mj,  M2,  etc.,  represent  the  different  instances  from  which 
the  inductions  are  made,  we  have  the  formula: 


M,,  as  well  as  M2, is  P; 

M1?  as  well  as  M2, is  S ; 

•         T?TTQ1-TT     Q     id      P 


Every  S  is  P. 

I.  Varieties  of  Induction, 

Inductions  are  divided  by  logicians  into  perfect  and  im- 
perfect. 

1.  The  so-called  perfect  induction  takes  place  "  when,  by 
a  perfect  enumeration  of  all  individuals  or  particulars,  the 
whole  sphere  of  the  universal  is  exhausted."     For  example: 

Mercury  revolves  on  its  axis  ;  so  do  Venus,  the  Earth,  Mars,  Jupiter, 
and  Saturn.  But  these  are  all  the  old  planets.  .'.  All  the  old  planets 
revolve  upon  their  axes. 

This,  however,  is  enumeration  and  addition  rather  than  inference. 
It  is  ordinarily  applicable,  of  course,  only  to  spheres  of  objects  so 
limited  that  all  the  individuals  may  be  successively  examined. 

2.  The  so-called  imperfect  induction  includes  the  cases 
in  which   the  general  is  reached  by  inference,  without  the 
complete  enumeration  of  objects.     Sometimes  only  a  very 
few  objects  out  of  an  indefinite  number  are  examined. 

The  conclusion  in  such  cases  may  be  made  universal,  first,  by  the 
pure  assumption  of  a  real  causal  nexus  between  the  subject  and  pre- 
dicate of  the  conclusion,  —  giving  what  may  be  called  an  inductive 
guess,  often  mistaken  for  induction  ;  or,  secondly,  by  the  strictly 
inductive  method  of  finding  some  real,  adequate  and,  if  possible,  true 
cause,  to  connect  the  subject  and  predicate  of  the  conclusion,  —  giving 
what  may  be  called  a  true  induction. 
14 


158  PRACTICAL    LOGIC. 

(1.)  The  inductive  guess  or  primary  induction  may  be  illustrated  by 
the  following  example : 

Iron  is  heavier  than  water,  so  is  silver,  quicksilver,  gold,  etc. 
/.  All  the  metals  are  heavier  than  water. 

The  primitive  inductions  thus  formed  are  mostly  false,  as  in  this 
example,  since  some  of  the  metals,  as  sodium  and  potassium,  are  lighter 
than  water.  A  vast  amount,  not  only  of  the  thinking  of  common 
life  but  also  of  the  so-called  scientific  induction,  is  of  this  nature,  and, 
therefore,  at  the  best  only  the  work  of  the  imagination,  and  at  the 
worst  mere  crude  guess-work. 

(2.)  The  true  induction  is  that  in  which  a  causal  nexus,  found  in 
the  nature  or  essential  relation  of  the  objects  examined,  is  more  or 
less  completely  established.  The  generalizations  in  such  cases  vary  in 
degree  of  probability.  The  highest  degree  of  probability  is  reached 
where  some  true  and  known  cause  is  at  work  producing  like  effects  in 
the  various  individual  instances.  The  probability  decreases  as  the 
cause  recedes  into  the  region  of  the  unknown  and  hypothetical.  The 
true  induction  may  be  illustrated  by  the  following  examples : 

Mercury,  Venus,  Jupiter,  etc.,  appear  to  be  wanderers  among  the  fixed  stars ; 

These  represent  all  the  planets  (since  this  apparent  wandering  is  due  to  the 
motion  of  these  stars  and  the  earth) ; 

.  • .  All  the  planets  will  probably  appear  to  be  wanderers  among  the.  fixed 
stars. 

3.  Analogy  has  already  been  shown  (p.  136)  to  involve 
both  induction  and  deduction,  the  inductive  being  the  prin- 
cipal element.  As  analogy  depends  upon  some  assumed 
likeness,  its  kinds  may  be  indicated  by  the  kinds  of  prop- 
erties (pp.  28-9)  in  which  the  likeness  is  found.  That  like- 
ness may  be  in  either  essential  or  non-essential  properties. 

(1.)  Analogy  based  upon  resemblance  in  essential  properties  is  the 

most  valuable  kind.  The  reasoning  in  this  case  rests  upon  the  generic 
and  essential  nature  of  the  objects  coordinated  in  the  analogy.  This 
may  be  illustrated  by  the  inference  made  by  Franklin  in  November, 
1749,  which  must  be  reckoned  among  inferences  from  analogy,  since 
lightning  and  electrical  phenomena  were  not  yet  known  to  be  the 
same  but  only  similar : 

"  The  electric  fluid,  as  it  shows  itself  in  experiments  made  by  us,  is  attracted 
by  projecting  metallic  points; 


THE  FORMATION    OF  REASONING.          159 

"  This  electric  fluid  and  lightning  agree  in  the  properties,  that  they  give  light 
of  the  same  color,  have  a  quick  motion,  are  conducted  by  metals,  etc.,  etc. ; 

"  Hence  it  is  to  be  presumed  that  lightning  will  also  be  attracted  by  project- 
ing metallic  points." 

(2.)  Analogy  based  upon  resemblance  in  peculiar  or  accidental  prop- 
erties is  of  comparatively  little  value,  since  these  properties  do  not 
indicate  any  essential  or  causal  principle  lying  back  of  them.  This 
may  be  illustrated  by  the  following  examples : 

"  The  American  swan  is  white;  therefore,  the  Australian  swan  is  white." 
"  John  Smith,  a  man  with  a  red  nose,  is  a  drunkard ;  therefore,  Timothy 
Jones,  another  man  with  a  red  nose,  is  a  drunkard." 

But  the  Australian  swan,  though  in  all  essential  respects  the  same 
as  the  American,  differs  in  the  non-essential  property  of  color,  being 
found  to  be  black.  In  like  manner  the  red  nose  may  be  the  result  of 
exposure  to  the  sun,  or  of  any  other  of  many  causes. 

(3.)  Analogy  based  upon  the  resemblance  of  relations  is  the  most 
difficult  to  deal  with  of  all  the  forms  of  analogy.  This  is  analogy  in 
the  strictest  sense.  It  is  necessary  in  all  inferences  of  this  kind  to 
consider  with  great  care  how  far  the  analogy  holds.  In  the  direct 
form  these  characteristics  of  analogy  may  be  illustrated  by  the  rela- 
tions of  a  foot  to  a  man  and  a  mountain.  It  is  under  the  man  as  a 
support  and  under  the  mountain  as  a  support,  but  its  being  that  upon 
which  man  walks  does  not  warrant  the  extension  of  this  relation  to 
the  foot  of  a  mountain.  Analogy  from  contradictories  is  illustrated 
when,  from  the  fact  that  virtue  produces  happiness,  it  is  inferred  by 
analogy  that  its  contradictory  moral  quality,  vice,  will  produce  unhap- 
piness. 

II.  Fallacies  in  Induction, 

The  most  common  fallacies  in  induction  arise  from  fail- 
ure, first,  in  dealing  with  the  facts ;  or,  secondly,  in  finding 
the  cause. 

The  most  common  fallacy  is  that  of  false  generalization 
(fictae  universalitatis,  or  unreal  universality*}.  This  makes  a 
show,  at  least,  of  complete  and  conclusive  induction. 

(1.)  This  may  result  from  careless  and  incomplete  observation  of  facts, 
and  may  then  be  called  the  fallacy  of  insufficient  observation.  Thus, 
a  French  physician,  it  is  said,  once  gave  a  Frenchman,  who  had 
typhoid  fever,  chicken  soup ;  the  patient  recovered,  and  on  the  basis 


160  PRACTICAL    LOGIC. 

of  this  one  fact  the  doctor  made  the  generalization,  —  "Chicken  soup 
will  cure  a  man  who  has  typhoid  fever."  He  afterwards  used  the 
same  remedy  in  the  case  of  an  Englishman  who  had  the  same  disease  ; 
the  patient  died,  and  the  doctor  reached  and  recorded  the  further  gen- 
eralization,— "  Chicken  soup  cures  a  Frenchman,  but  kills  an  English- 
man." 

(2.)  The  false  generalization  may  also  result  from  the  hasty  assump- 
tion of  something  as  the  cause  which  is  not  the  cause  (non  causa  pro 
causa}.  That  which  is  assumed  as  the  cause  in  such  cases  may  be 
either  a  simple  concomitant  or  a  mere  antecedent  (post  hoc  ergo  propter 
hoc).  The  fallacy  of  assuming  that  a  simple  concomitant  is  a  cause 
(cum  hoc  ergo  propter  hoc)  is  illustrated  by  the  conclusion  of  the 
materialist,  that  since  chemical  action  in  the  brain  accompanies  mental 
action,  it  is  the  cause  of  mental  action ;  which  is  paralleled  by  the 
assumption,  that  because  the  small  boy's  boots  always  accompany  the 
small  boy,  therefore,  they  are  the  small  boy.  The  fallacy  of  assuming 
that  a  mere  antecedent  is  a  cause  (post  hoc  ergo  propter  hoc)  is  illus- 
trated by  the  inference,  among  the  ancient  Romans,  that  when  a 
general  engaged  the  enemy  where  the  response  of  the  augurs  had  been 
unfavorable,  and  suffered  defeat,  the  cause  of  the  disaster  was  the 
unfavorable  character  of  the  auspices. 

Praxis. —  Test  the  following  conclusions  reached  by  induction ;  state 
whether  the  induction  is  valid  or  not  in  each  case ;  verify  the  induction 
when  valid,  and  when  not  valid  show  what  is  the  fallacy  involved : 

1.  "  The  Jews  are  rogues,— The  Carthaginians,  faithless,— The  Cretans,  liars, 
— The  French,  braggadocios, — The  Germans,  mystics, — The  rich,  purse-proud, — 
The  noble,  haughty, — Women,  frivolous, — The  learned,  pedants."  2.  Matter 
is  eternal.  3.  Spirit  is  essentially  immortal.  4.  The  Irish  are  malcontents.  5. 
All  human  languages  had  a  common  origin.  6.  The  great  civilizations  have 
all  flourished  in  the  North  Temperate  Zone.  7.  Man  is  what  circumstances 
make  him.  8.  "  There 's  a  divinity  that  shapes  our  ends,  rough  hew  them  how 
we  will."  9.  That  which  survives  is  fittest.  10.  All  the  planets  revolve  on 
their  axes.  11.  Conceited  men  are  always  shallow.  12.  Ignorant  men  are  con- 
ceited. 13.  Selfish  men  are  not  men  of  principle.  14.  Man  is  born  sinful.  15. 
The  Christian  nations  are  the  progressive  nations.  16.  The  Protestant  nations 
are  the  foremost  nations  in  the  world.  17.  The  reach  of  gravitation  is  univer- 
sal. 18.  The  best  education  is  secured  by  means  of  the  Classics.  19.  The  best 
education  is  secured  by  means  of  the  Natural  Sciences.  20.  The  best  edu- 
cation is  secured  by  means  of  the  combined  study  of  the  Classics,  Natural 
Sciences,  and  Mathematics.  21.  The  appearance  of  a  comet  is  the  harbinger 
of  famine,  pestilence,  and  war.  22.  Friday  is  an  unlucky  day. 

State,  in  the  following  cases,  whether  the  facts  are  exceptional,  and, 
if  so,  to  what  class  each  belongs ;  and  show  whether  and  how  they 


eTHE  \ 

RSITY   J 
RMATION   OF  REASONING.         161 

can  be  reconciled  with  the  hypotheses  to  which  they  appear  to  be  ex- 
ceptional : 

1.  The  rotation  of  the  earth  upon  its  axis  gives  to  all  the  stars  an  apparent 
motion  of  rotation  from  east  to  west.  The  Pole  Star  seems  not  so  to  revolve. 
2.  According  to  the  Newtonian  view  of  gravitation  all  bodies  are  heavy.  But 
flame,  bubbles,  clouds,  etc.,  ascend,  and  were,  therefore,  regarded  by  the  an- 
cients as  essentially  light.  3.  The  Copernican  theory  teaches  that  the  earth  in 
revolving  moves  toward  the  east  at  the  rate  of  a  thousand  miles  or  more  an 
hour.  It  has  been  objected  to  it  that,  if  this  be  so,  then  a  stone  dropped  from 
the  topmast  of  a  ship  at  anchor  ought  to  fall  behind  toward  the  west,  just  as  a 
stone  dropped  from  the  mast-head  of  a  moving  ship  would  fall  behind,  owing 
to  the  motion  of  the  ship.  4.  The  ancients  held  that  the  general  tendency  of 
bodies  on  the  earth  is  downward.  In  the  case  of  the  loadstone  held  over  iron, 
the  iron  had  a  tendency  upward.  This  could  not  be  explained  by  the  hypoth- 
esis of  essential  lightness,  since  iron  is  one  of  the  heaviest  substances.  5. 
According  to  the  theory  of  Torricelli  and  Pascal,  the  mercury  ought  to  stand 
at  a  height  of  about  31  inches  in  the  barometer.  Boyle  showed  that  in  a 
perfectly  cleansed  tube  it  could  be  made  to  stand  as  high  as  75  inches.  6. 
According  to  the  hypothesis  of  the  materialistic  evolutionist,  the  development 
of  the  universe  has  been  a  continuous  change  and  progress  from  the  primor- 
dial atom,  without  break  or  interference  of  any  other  than  material  forces. 
Dr.  McCosh,  in  Christianity  and  Positivism  (Appendix,  p.  344),  enumerates 
eleven  breaks  in  the  continuity,  among  which  are  the  following :  "  Chemical 
action  cannot  be  produced  by  mechanical  power."  "  Life,  even  its  lowest 
forms,  cannot  be  produced  from  unorganized  matter."  "  Protoplasm  can  be 
produced  only  by  living  matter."  "A  living  being  can  be  produced  only  from 
a  seed  or  germ."  "An  animal  cannot  be  produced  from  a  plant."  "  Sensation 
cannot  be  produced  by  insentient  matter."  The  genesis  of  a  new  species  of 
plant  or  animal  has  never  come  under  the  cognizance  of  man,  either  directly 
or  indirectly.  Consciousness  cannot  be  produced  out  of  mere  matter  or  sensa- 
tion. "  We  have  no  knowledge  of  man  being  generated  out  of  the  lower  ani- 
mals." "All  human  beings,  even  savages,  are  capable  of  forming  certain  high 
ideas,  such  as  those  of  God  and  duty ;"  the  brute  is  not. 

State  and  test  the  following  hypotheses : 

1.  The  Wolffian  hypothesis  of  the  origin  of  the  Homeric  Poems.  2.  The 
hypotheses  concerning  the  origin  of  the  Four  Gospels.  3.  The  hypotheses 
concerning  the  nature  of  Electricity.  4.  The  hypotheses  concerning  the 
nature  of  Heat.  5.  The  hypotheses  concerning  the  composition  of  Comets. 
6.  The  hypotheses  concerning  the  origin  of  Life  on  our  globe.  7.  The  hypoth- 
eses concerning  the  nature  of  Man.  8.  The  hypotheses  concerning  the  nature 
of  Beauty.  9.  The  hypotheses  concerning  the  origin  of  the  Universe. 

Note.— For  a  complete  and  extended  treatment  of  Induction,  the  teacher 
and  student  are  referred  to  the  following  works :  Jevon's  Principles  of  Science; 
Mill's  System  of  Logic,  Ratiocinative  and  Inductive. 
14*  L 


162  PRACTICAL    LOGIC. 


CHAPTER    II. 

THE  UNFOLDING  OF  REASONING  OR  THB 
SYLLOGISM. 

THE  treatment  of  the  formation  of  reasoning  is  naturally 
followed  by  the  consideration  of  the  unfolding  and  testing 
of  its  various  kinds,  as  embodied  in  the  Syllogism,  and  the 
presentation  of  the  various  forms  of  Fallacy  or  unsound 
reasoning. 

Practical  Logic  should  train  the  thinker  to  distinguish 
readily  between  a  true  syllogism  and  one  that  only  seems 
to  be  a  true  one.  This  requires  the  treatment,  in  successive 
Sections,  of  the  Forms  and  Tests  of  Categorical  and  Hypo- 
thetical Syllogisms,  and  the  kinds  of  Fallacies. 

Section  I,— The  Categorical  Syllogism  Unfolded, 
In  unfolding  the  categorical  syllogism,  the  nature  and 
kinds  of  which  have  already  been  presented  (p.  141),  the 
following  Topics  will  be  considered : 

Topio  I, — The  Possible  Forms  of  the  Syllogism,  or  Figure  and  Mood. 
Topic  II.— The  Testing  of  the  Valid  Forms. 
Topio  III. — Complex  and  Abnormal  Forms. 

Topic  First.— -The  Possible  Forms  of  the  Simple  Categor- 
ical Syllogism. 

The  possible  forms  of  the  single  syllogism  are  determined 
by  the  various  positions  of  the  middle  term,  in  the  premises, 
with  reference  to  the  major  and  minor  terms,  and  the  pos- 
sible combinations  of  the  four  normal  judgments,  A,  E,  I, 
0,  in  groups  of  three.  The  first  gives  rise  to  Figure,  the 
second  to  Mood. 

I.  Figure  of  Syllogisms. 

Syllogisms  are  divided  into  different  Figures  by  the  posi- 


THE    UNFOLDING    OF  REASONING.        163 

tion  of  the  middle  term.     The  possible  positions  are  four, 

which  give  rise  to  as  many  Figures : 

Figure  I,     middle  term  subj.  of  maj.  prem.  and  pred.  of  minor. 
Figure  II,         "         "     pred.  of  both  maj.  and  min.  premises. 
Figure  III,       "        "     subj.     "  "       "       " 

Figure  IV,        "         "     pred.  of  maj.  prem.  and  subj.  of  minor. 
This  may  be  expressed  and  illustrated  as  follows : 

f     M  *  P     Every  virtue  is  praiseworthy  ;  =  A 

l%'    '    J      g  ^  M     Eloquence  is  a  virtue ;  =  A 


ig.  I.      f 

b  prae.   j 


P  /.  Eloquence  is  praiseworthy.  =  A 

f     P  ^|- M     No  vice  is  praiseworthy ;  =  E 

l%'      \   4      S  •  M     Eloquence  is  praiseworthy ;  =  A 

prae  prae.  [  ^  g  ^ p  ^  Eloquence  is  not  a  yice  ==  E 

f     M  *  P     Every  virtue  is  praiseworthy ;  =  A 

sub  sub.    [  ^  g  ^ p  ^  gomething  useful  is  praiseworthy.    =  I 

c     P  ^          M     Every  virtue  is  praiseworthy ;          —  A 

lg'      'X      M  •  S      Everything  praiseworthy  is  useful ;  =  A 

prae  sub.    ^  .  g  ^ p  .  gomething  usefoi  is  a  virtue.  =  I 

In  these  examples  the  mnemonic  sub  and  prae  stand  for  subject  and 
predicate.  The  wedge-shaped  figure  or  line  (^ — )  denotes  a  judg- 
ment. Its  thick  end  turns  toward  the  subject  of  extension,  which  is 
contained  as  a  species  under  the  predicate  as  a  genus.  The  perpendic- 
ular stroke  drawn  through  the  line  (^ )  indicates  negation.  In 

the  Hamiltonian  Notation,  of  which  this  is  a  part,  the  heavy  horizon- 
tal line  (••••)  used  in  the  unfigured  syllogism  (p.  165),  indicates 
equality  between  subject  and  predicate,  or  a  substitutive  judgment. 

Note.— The  syllogisms  ordinarily  used  in  the  examples  in  Logic  are  made 
up  of  propositions  of  extent,  and  are,  therefore,  called  extensive  syllogisms. 
Hamilton  introduces  and  insists  upon  the  intensive  syllogism.  This  is  ex- 
pressed by  reversing  the  wedge-shaped  figure,  which  in  this  case  represents 
the  copula  as  meaning  "comprehends,"  instead  of  "is  contained  under," 
which  is  its  meaning  in  the  extensive  syllogism.  The  two  forms  may  be  illus- 
trated : 

The  notion  responsible  is  contained  under  the  notion  free- 
agent;  M»  P 
The  notion  man  is  contained  under  the  notion  responsible 
agent ;                                                                                    S  »           M 


The  notion  man  is  contained  under  the  notion  free- 
agent.  .'.  S  i 


164  PRACTICAL    LOO  1C. 

•jj,  (  The  notion  man  comprehends  the  notion  responsible ; 
*  -I  The  notion  responsible  comprehends  the  notion  free ; 
t:  [  .-.  The  notion  man  comprehends  the  notion  free. 

In  the  first  form  the  notions  are  class  notions;  in  the  second,  concepts  proper. 
In  the  second  form  the  premises  of  the  first  form  are  transposed.  With  this  slight 
change  extensive  and  intensive  syllogisms  conform  to  the  same  rules,  and  are 
so  nearly  identical  that  the  intensive  form  does  not  need  separate  treatment. 
In  fact,  both  propositions  of  extent  and  of  content  are  often  used  in  the  same 
syllogism.  Thus: 

All  of  the  metals  are  positive ;  Proposition  of  content. 

Silver  is  one  of  the  metals ;  Proposition  of  extent. 

/.  Silver  is  positive.  Proposition  of  content. 

II,  Mood  of  Syllogisms. 

The  Mood  of  a  Syllogism  is  the  arrangement  of  its  prop- 
ositions according  to  their  respective  quantity  and  quality. 
There  are  as  many  possible  Moods  as  there  are  combinations 
of  the  four  normal  propositions,  A,  E,  I,  0,  in  syllogistic 
form. 

It  will  be  seen  on  examination  that  in  the  premises  each  of  the  four 
may  be  placed  first,  and  then  followed  by  each  of  the  four  successively, 
giving  4X4  =  16  combinations.  Each  of  these  16  combinations  may 

then  be  followed  successively  in  the 
The  16  Premise  Forms.          conclusion  by  each  of  the  four  judg. 

AE        EE        IE        OE    ™>>te,  A,  E,  1,0,  giving  16X4  =  64 

possible  syllogistic  combinations.  These 
forms  will  be  presented  later,  in  gath- 
ering up  the  results  of  the  application 

of  the  Rules,  and  need  not,  therefore,  be  here  given.     The  student, 
moreover,  will  be  able  readily  to  form  the  combinations  for  himself. 

It  will  be  found,  when  the  proper  tests  are  applied,  that  compar- 
atively few  of  these  combinations  give  valid  syllogisms. 

Topic  Second.  —  The  Testing  of  the  Valid  Forms. 

Two  methods  have  been  employed  in  testing  the  validity 
of  the  various  combinations : 

First,  By  what  Hamilton  calls  "  the  thorough-going  quan- 
tification of  the  predicate." 

Second,  By  comparing  the  spheres  of  the  notions  in  the 


THE  UNFOLDING  OF  REASONING.    165 

various  combinations  and  framing  and  using  Rules  based 
upon  the  results.     This  is  the  logical  method. 

ist.  The  Unfigured  Syllogism.  — By  quantifying  the  predicate,  Hamilton 
has  sought  to  dispense  with  Figure  altogether.  By  the  explicit  quantification 
of  the  terms  the  exact  quantity  of  each  is  brought  out.  After  the  quantifica- 
tion the  relation  between  the  terms  of  the  judgments  may,  according  to  Ham- 
ilton, be  expressed  by  the  sign  of  equality,  and  the  subject  and  predicate  may 
indifferently  change  places.  The  figured  and  unfigured  form  may  be  illustrated 
by  example : 

Figured. —Fig.  I.  Unfigured. 

A  Men  are  rational ;  All  men  =  some  rational ; 

A  Negroes  are  men ;  All  negroes  =  some  men ; 

A          .'.  Negroes  are  rational.  .'.  All  negroes  =  some  rational. 

If  the  object  in  introducing  this  new  method  is  to  simplify  reasoning  i*,  is 
not  attained,  since  while  it  apparently  simplifies  it  really  complicates  it.  The 
fatal  objection  to  its  general  introduction  is  found  in  the  fact,  that  the  instant 
the  predicate  of  a  judgment  is  quantified,  it  ceases  to  be  a  logical  or  qualitative 
•whole  and  becomes  a  simple*  quantitative  or  mathematical  whole.  The  judgment 
is  no  longer  a  logical,  but  a  simple  mathematical,  judgment.  Davis  enforces  this 
position  in  "  The  Theory  of  Thought,"  p.  124: 

"  For,  consider  the  meaning  of '  all '  in  the  predicate.  It  is  not,  it  cannot  be, 
the  distributive,  divisive,  exemplar  '  all,'  but  is  always  the  total,  indivisible, 
cumular  '  all,'  a  mathematical  whole.  E.  g.,  'All  men  are  bimana ;'  this  is 
the  distributive  '  all,'  meaning  that  all,  each,  and  every  man  is  in  the  class,  or 
has  the  mark,  bimana.  But  let  us  say  'All  men  are  all  bimana ;'  this  does  not 
mean  '  Every  man  is  all  bimana,'  nor  'All  men  are  every  bimana,'  nor '  Every 
man  is  every  bimana,'  which  is  nonsense.  It  means  'All  men  (as  a  mathemat- 
ical, total,  collective  whole)  are  all  bimana'  (as  ditto).  Thus  '  all'  in  the  "pred- 
icate is  never  distributive,  but  cumular,  and  enforces  the  '  all '  of  the  subject 
also  to  be  cumular.  So  also  the  total  predicate  of  a  negative  is  a  mathemat- 
ical, not  a  distributed  total ;  and  '  some '  in  the  predicate  is  a  mathematical 
part.  More  generally,  whenever  the  quantity  of  the  predicate  is  designated, 
both  terms  are  individuals,  and  the  judgment  is  mathematical." 

The  decision  whether  a  given  combination  leads  to  a  valid  inference,  and 
the  proof  of  the  validity  or  non-validity,  must  depend  upon  the  comparison 
of  the  spheres  of  the  notions  as  given  in  the  premises  of  the  apparent  syllo- 
gism. The  reciprocal  relations  of  notions,  already  presented  (pp.  40  and  45), 
comprehend  all  the  relations  essential  in  the  comparison  of  notions  in  reason- 
ing. These  relations,  as  has  been  seen,  may  be  made  apparent  to  the  senses 
by  the  use  of  geometrical  figures. 

2d.  The  proper  method  of  testing  the  validity  of  the 
various  combinations  of  judgments  as  premises  is  by  com- 
paring the  spheres  of  the  notions  involved  in  these  judg- 
ments. The  valid  forms  are  determined  by  General  Princi- 
ples arising  out  of  the  Logical  Axioms ;  by  General  Rules 


166  PRACTICAL    LOO  1C. 

arising  out  of  the  relations  of  the  terms  and  propositions 
of  the  Syllogism ;  and  by  Special  Canons  arising  out  of  the 
nature  of  the  particular  Figures.  Figure  I.  has  always  been 
considered  the  normal  form  of  the  syllogism,  to  which  the 
other  forms  may  be  reduced.  Hence,  the  principles  which 
govern  the  Reduction  of  Syllogisms  to  this  Figure  need  to 
be  presented.  For  convenience  of  reference,  a  Conspectus 
of  Results  will  also  be  given. 

I.  The  General  Principles. 

At  the  foundation  and  applying  equally  to  all  the  figures 
are  three  general  principles  embodying  the  axiom  of  Iden- 
tity or  Affirmation  and  of  Contradiction  or  Negation. 

First  General  Principle.  Affirmative  Conclusion. — If,  when  the 
major  and  minor  terms  are  compared  with  the  same  middle  term,  they 
both  agree  with  it,  they  may  agree  with  each  other.  This  is  the  basis 
of  affirmative  conclusions. 

Second  General  Principle.  Negative  Conclusion. — If,  on  such  com- 
parison, one  term  agrees  and  the  otfear  disagrees  with  the  same  middle 
term,  they  disagree  with  each  other.  This  is  the  basis  of  negative 
conclusions,  which,  therefore,  result  from  the  combination  of  one  af- 
firmative and  one  negative  premise. 

Third  General  Principle.  No  Conclusion. — If,  on  such  comparison, 
both  terms  disagree  with  the  same  middle  term,  it  is  uncertain  whether 
they  agree  or  disagree  with  each  other,  and,  therefore,  no  valid  infer- 
ence can  be  drawn  in  such  cases.  This  is  the  case  where  both  prem- 
ises are  negative. 

II.  The  General  Rules. 

The  general  rules  arising  out  of  these  general  principles 
depend  upon  the  relations  of  the  terms  and  propositions  of 
the  syllogism.  They  may  be  reduced  to  seven,  and  are 
equally  applicable  to  all  the  figures. 

Rule  1st. — There  must  be  three,  and  only  three,  terms  in  any  valid 
syllogism.  The  major  and  minor  terms  would  not  otherwise  be  logi- 
cally connected  at  all.  This  needs  no  illustration.  It  guards  against 
the  common  Fallacy  of  Four  Terms,  which  oftenest  arises  from  the  use 


THE  UNFOLDING  OF  REASONING.    167 

of  equivocal  terms  (p.  82)  or  want  of  clear  thought.     In  all  cases  the 
middle  term  needs  to  be  carefully  examined  in  order  to  make  sure  that 
it  is  used  in  precisely  the  same  sense  in  both  premises.     Whenever  it 
is  not  so  used  the  case  is  one  of  substantially  four  terms.     E.  g. » 
"  What  we  eat  grows  in  the  fields  or  is  the  flesh  of  animals ; 

Cooked  food  is  what  we  eat ; 
/.  Cooked  food  grows  in  the  fields  or  is  the  flesh  of  animals." 

This  is  a  case  of  two  middle  terms.  In  one  premise,  "  what  we  eat" 
is  used  with  reference  to  its  mere  essence ;  in  the  other,  with  reference 
to  the  accident  or  property  of  being  cooked.  This  is  the  Fallacy  of 
Accident  (Fallacia  Accidentis). 

Rule  2d. — The  middle  term  must  be  distributed  at  least  once.  The 
necessity  for  this  arises  from  the  fact  that  without  it  the  major  and 
minor  terms  might  be  compared  with  different  parts  of  the  sphere  of 
the  middle  term,  and  so  fail  of  being  brought  into  logical  connection. 
E.g.: 

All  poets  (P)  are  men  (M) ;     =  A 

All  orators  (S)  are  men  (M).  =  A 

We  cannot  infer  that  "  All  poets  are  orators,"  or  that  "Some  poets 
are  orators,"  since  the  universal  affirmative,  A,  does  not  distribute  the 
predicate  (p.  115),  which  is  here  the  middle  term.  Such  conclusions 
would  result  in  the  Fallacy  of  Undistributed  Middle. 

Rule  3d.— A  term  undistributed  in  the  premises  must  not  be  dis- 
tributed in  the  conclusion.  Otherwise  the  conclusion  would  include 
more  than  is  involved  in  the  premises.  The  violation  of  this  rule  is 
called  the  Fallacy  of  Illicit  Process.  The  fallacy  may  occur  either 
with  the  major  term  or  with  the  minor. 

Illicit  Process  of  the  Major  Term. 

All  birds  (M)  are  winged  (P) ;  =  A 
A  bat  (S)  is  not  a  bird  (M) ;       =  E      ($) 
.'.  A  bat  (S)  is  not  winged  (P).      =  E 
The  major  term,  "  winged,"  is  undistributed  in  the  major  premise 
(A),  and  distributed  in  the  conclusion  (E).     Hence  the  inference  is  not 
valid,  as  may  be  seen  from  the  above  presentation  of  the  relation  of 
the  spheres  of  the  notions. 

Illicit  Process  of  the  Minor  Term. 

Persons  without  imagination  (M)  are  not  true  poets  (P) ;  =  E 

Good  logicians  often  (S)  are  without  imagination  (M) ;       =  I 

.'.  Good  logicians  (S)  are  not  true  poets  (P).  =  E 


168  PRACTICAL    LOGIC. 

In  this  case  the  word  "  often"  makes  the  judgment  equivalent  to, 
"  Some  good  logicians  are  not  true  poets ;"  while  the  universal  neg- 
ative conclusion  denies  of  "all  good  logicians"  that  they  are  "true 
poets." 

Rule  4th. — The  conclusion  must  always  follow  the  weaker  part. 
By  this  is  meant  that,  if  one  premise  is  negative  the  conclusion  must 
be  negative,  and,  if  one  premise  is  particular  the  conclusion  must  be 
particular.  This  does  not  need  illustration. 

It  follows  that  universal  conclusions  can  be  reached  only  from  uni- 
versal premises.  It  will  appear  subsequently  that  universal  conclu- 
sions are  not  warranted  in  all  cases  by  universal  premises,  since  they 
would  often  involve  the  fallacies  of  undistributed  middle  or  of  illicit 
process. 

Rule  5th. — No  valid  inference  can  be  drawn  where  both  premises 
are  negative.  This  follows  from  the  Third  General  Principle.  The 
relation  of  the  major  and  minor  terms  to  each  other  is  left  wholly  un- 
determined by  the  form  of  the  judgment. 

Three  cases  come  under  this  Rule :  where  both  premises  are  universal  neg- 
ative ;  where  one  is  universal  negative  and  the  other  particular  negative ; 
where  both  are  particular  negatives.  The  Rule,  therefore,  excludes,  as  invalid 
in  all  instances,  four  of  the  sixteen  possible  combinations,— E  E,  E  O,  O  E,  0  O,— 
leaving  only  twelve  possibly  valid  combinations. 

A  single  illustration,  coming  under  the  first  case,  will  suffice  to  assist  the 
student  in  presenting  for  himself  in  diagram  the  various  forms  which  the  in- 
determinate relations  of  the  major  and  minor  terms  may  take. 
No  poets  (P)  are  angels  (M) ;       No  P  is  M ;  =  E 
No  men  (S)  are  angels  (M) ;         NoSisM;  =E 


By  the  terms  of  the  judgments  both  "  poets"  and  "  men  "  are  excluded  from 
"  angels,"  but  they  may  stand  to  each  other  in  any  one  of  at  least  the  five  fol- 
lowing relations  (p.  40)  :  1st.  They  may  be  independent  or  coordinate.  2d. 
They  may  be  coextensive.  3d.  S  may  include  P.  4th.  P  may  include  S.  5th. 
S  and  P  may  intersect  each  other. 

2 


It  will  be  found  that,  in  the  second  and  third  cases  of  negative  premises,  the 
possible  relations  of  the  terms  become  even  more  complicated. 

Rule  6th.  —  No  valid  inference  can  be  drawn  where  both  premises 
are  particular.  In  such  instances  the  precise  connection  of  the  spheres 
of  the  major  and  minor  terms  with  that  of  the  middle  cannot  be  deter- 
mined from  the  form  of  the  judgments. 


THE    UNFOLDING    OF  REASONING.         169 

Three  cases  come  under  the  Rule :  where  both  premises  are  particular  affir- 
mative ;  where  one  is  particular  affirmative  and  the  other  particular  negative ; 
where  both  are  particular  negative. 
The  first  case,  1 1,  will  furnish  a  sufficient  illustration. 

Some  poets  (M)  are  intellectual  (P) ;    Some  M  is  P ;     =1 
Some  poets  (M)  are  emotional  (S) ;      Some  M  are  8;  •=  I 


In  this  case  the  "  intellectual "  and  "  emotional "  poets  might  stand  in  either 
of  the  following  relations :  1st.  They  might  exactly  coincide.  2d.  They  might 
wholly  exclude  each  other.  3d.  They  might  intersect  each  other,  etc. 

3 

"f '"  i  \ 

etc. 


The  same  indeterminateness,  in  the  relation  of  the  major  and  minor  terms 
to  each  other  through  the  middle  term,  may  be  shown  to  exist  in  the  other 
cases.  The  third  case  is  likewise  excluded  from  valid  syllogistic  forms  by  the 
Rule  for  negative  premises. 

The  Rule,  therefore,  excludes  three  combinations  not  excluded  by  the  pre- 
vious Rule :  1 1, 1  O,  O  I ;  leaving  but  nine  possibly  valid  combinations. 

Apparent  Exceptions. — Two  apparent  exceptions  to  this  Rule  need 
to  be  noted:  first,  syllogisms  involving  plurative  judgments  (p.  114); 
secondly,  those  in  which  one  or  both  of  the  premises  are  substitutive 
judgments  (p.  113).  These  are  not,  of  course,  strictly  particular 
judgments. 

Plurative  Judgments,  whether  indefinite  or  numerically  definite,  give 
valid  conclusions,  as  seen  in  the  following  examples : 

Most  men  (M)  are  conceited  (P) ;      A     Ignorailt 1 D 

I  r>  L> 

Conceited. 
Most  men  (M)  are  ignorant  (S) ;        E    Ignorant  and  conceited.  | Q 

/.  At  least  some  conceited  men  (S)  are  ignorant  (P). 

It  is  obvious  in  this  case  that  "  most  men  "  in  the  major  premise  may  coin- 
cide more  or  less  fully  with  "most  men"  in  the  minor,  as  illustrated  in  the 
diagrams.  In  the  first  case,  the  line  A  C  represents  the  "  ignorant,"  B  D  the 
"  conceited,"  and  AD"  all  men."  The  line  B  C  represents  the  minimum  of 
agreement,  in  the  given  case,  when  the  "  ignorant"  and  "  conceited"  differ  to 
the  utmost.  In  the  second  case,  E  F  represents  both  the  "  ignorant"  and  the 
"  conceited,"  and  EG"  all  men."  The  line  E  F  represents  the  maximum  of 
agreement,  when  the  "ignorant"  and  "conceited"  agree  to  the  utmost,  i.  e., 
coincide. 

If  this  be  given  the  numerically  definite  or  proportional  form,  it  may  become 

80  out  of  every  100  men  are  conceited ; 

80  out  of  every  100  men  are  ignorant ; 
:.  At  least  60  out  of  every  100  conceited  men  are  ignorant. 
15 


170  PRACTICAL    LOGIC. 

In  this  instance  the  "80"  of  the  major  premise  may  agree  more  or  less  fully 
with  the  "  80  "  of  the  minor,  as  illustrated  by  the  diagram.  The  minimum  of 
agreement,  as  shown  in  the  following  diagram,  is  D  B,  or  60  out  of  every  100 ; 
the  maximum,  E  F,  80  out  of  every  100. 

Ignorant  =  80  B  Ignorant-conceited  =  80 

I      I      I      I      I      I      I      I      1      I      I          I      I      I      I      I      I      I      I      I      I      I 
A       D  |  Conceited  =  80  C        E  |  F       G 

Substitutive  Judgments,  even  when  particular  (Y),  often  result  in 
making  conclusions  valid  that  would  be  invalid  if  the  premises  were 
mere  particular  attributives.  Such  judgments,  whether  universal  or 
particular,  always  distribute  the  predicate  (p.  115).  They  are  not,  how- 
ever, strictly  particular  judgments.  For  example : 

Some  trees  (P)  are  (all  the)  oaks  (M) ;  =  Y  Some  P  is  all  M ; 

Some  oaks  (M)  are  white  oaks  (S) ;         =  I  or  Y       Some  M  is  (all)  S; 
/.Some  white  oaks  (S)  are  trees  (P).         =  I  .-.  All  S  is  P. 

Eule  7th. — No  valid  inference  can  be  drawn  from  the  combination 
of  a  particular  major  premise  with  a  negative  minor  premise.  This 
will  appear  from  the  comparison  of  the  spheres  of  the  notions  in  the 
four  possible  cases :  IE;  OE;  10;  00. 

The  Rule  may  be  sufficiently  illustrated  by  the  first  case,  I  E.  The  other 
combinations  have  also  been  already  excluded  from  the  valid  combinations,— 
O  E  and  O  O  by  negative  premises ;  I  O  and  O  O  by  particular  premises. 

Some  iron  ores  (P)  are  magnetic  (M) ;  =  I 
No  lead  ores  (S)  are  magnetic  (M) ;      =  E 


It  is  not  determined  whether  the  sphere  of  S  is  quite  separated  from  the  sphere 
of  P,  or  intersects  it,  or  falls  wholly  within  it.  If  the  attempt  were  made  to 
draw  the  conclusion,  "  No  lead  ores  are  iron  ores,"  the  negative  would  dis- 
tribute the  predicate,  "iron  ores"  (P),  which  is  not  distributed  in  the  major 
premise,  and  would  thus  result  in  illicit  process  of  the  major  term. 

This  Rule,  therefore,  excludes  the  combination  I  E,  and  leaves  only  eight  out 
of  sixteen,  which  can  be  valid  in  any  case.    These  may  be  stated  (numbered 
for  convenient  reference  in  treating  the  four  Figures)  as  follows : 
1.  A  A.    2.  E  A.    3.  I  A.    4.  O  A.  Only  part  of  the  remaining  eight  will 

5.  A  E.  be  found  to  hold  true  in  any  one  of  the 

6.  A  I.     7.  E  I.  Figures. 
8.  A  O. 

III.  Special  Canons  of  the  Figures. 

Each  of  the  four  Figures  has  its  special  rules  resulting 
from  the  relations  of  the  terms,  which  may  be  embodied  in 
a  Canon  for  that  Figure. 

1.  Figure  I.  is  that  which  has  the  middle  term  as  the  sub- 


THE    UNFOLDING    OF   REASONING.         171 

ject  of  the  major  premise  and  the  predicate  of  the  minor. 
There  follows,  from  the  resulting  relations  of  the  terms, — 

Canon  1st. — In  Figure  I.  the  requirements  are  : 
f  Major  prem.  universal  to  avoid  fallacy  of  undistributed  middle; 

1  Minor  prem.  affirmative  to  avoid  fallacy  of  illicit  process  of  maj.  term. 
Testing  by  this  Canon  the  eight  possible  combinations  left  by  the 

General  Rules,  only  six  syllogistic  forms  are  found  valid  in  Figure 
I.:  AAA,  AAI,  EAE,  EAO,  All,  EIO.  These  are  reducible  to  four, 
since  AAI  and  EAO  are  but  cases  of  particular  or  weakened  conclu- 
sions, included  in  the  universals,  AAA  and  EAE. 

Note.— In  this  Figure  the  process  of  testing  by  the  General  Rules  and  the 
Canon  will  be  applied  to  the  eight  combinations  successively,  in  order  to  pre- 
pare the  student  to  apply  the  like  process  to  the  remaining  three  Figures. 

No.  i,  A  A,  by  the  successive  addition  of  the  four  propositions,  A,  E,  I,  O, 
gives  AAA,  AAE,  AAI,  AAO.  The  second  and  fourth  of  these  forms,  AAE, 
AAO,  drop  out  since  the  affirmative  premises  indicate  agreement,  while  the 
negative  conclusion  would  infer  disagreement.  The  third,  AAI,  is  included 
in  AAA.  Only  one  valuable  form,  AAA,  remains.  It  conforms  to  the  Canon, 
since  its  major  premise  is  universal  and  its  minor  premise  affirmative,  and  the 
syllogism  thus  guarded  against  fallacy.  This  valid  mood  is  known  among 
logicians  by  the  mnemonic  word,  Barbara,  the  meaning  of  the  consonants  in 
which  will  be  subsequently  explained  under  Reduction.  It  is  illustrated  in 
the  following  example : 

2  All  that  is  composite  is  dissoluble ;  =  A       All  M  is  P; 
ja      All  material  things  are  composite ;  =  A       All  S  is  M ; 
«  .-.  All  material  things  are  dissoluble.  =  A   /.  All  S  is  P. 

No.  a,  E  A,  by  the  successive  addition  of  the  four  propositions,  A,  E,  I,  O, 
gives  EAA,  EAE,  EAI,  EAO.  The  first  and  third  of  these  forms,  EAA  and 
EAI,  drop  out,  since  the  one  negative  premise  always  requires  a  negative  con- 
clusion by  Rule  4th.  The  fourth,  EAO,  is  included  in  EAE,  drawing  a  partic- 
ular conclusion  when  the  universal  is  permissible.  The  valid  mood,  EAE,  is 
known  among  logicians  by  the  mnemonic  word,  Celarent.  It  stands  the  test 
of  the  Canon.  It  is  illustrated  in  the  following  example : 

No  finite  being  is  exempt  from  error ;  =  E       No  M  is  P ;  ~ 

g       All  men  are  finite  beings ;  =  A      All  S  is  M ; 

"5  /.  No  man  is  exempt  from  error.  =  E  .-.  No  S  is  P. 

No.  3, 1  A,  gives  IAA,  IAE,  IAI,  IAO,  none  of  which  are  valid,  since,  besides 
the  breach  of  the  General  Rules,  the  particular  major  premise,  I,  violates  the 
Canon,  and  always  results  in  undistributed  middle. 

No  4,  OA,  gives  OAA,  OAE,  OAI,  OAO,  none  of  which  are  valid  for  the  rea- 
sons given  under  No.  3. 

No.  5,  AE,  gives  AEA,  AEE,  AEI,  AEO,  none  of  which  are  valid,  since  the 
negative  minor  premise,  E,  violates  the  Canon,  and  results  in  illicit  process  of 
the  major  term. 


172  PRACTICAL    LOO  I C. 

No.  6,  A  I.  gives  AIA,  AIE,  All,  AIO.  The  first  form,  AIA,  violates  Rule 
4th ;  the  second  and  fourth,  AIE  and  AIO,  violate  the  General  Principle  of  all 
affirmatives.  The  fourth,  All,  is  valid,  standing  the  test  of  the  Canon.  The 
valid  mood  is  known  among  logicians  by  the  mnemonic  word,  Darii.  It  is 
illustrated  as  follows : 

X  p 

..:      All  virtues  are  laudable ;  =  A       All  M  is  P ; 
£      Some  habits  are  virtues ;   =  I        Some  S  is  M ; 
Q  .'.  Some  habits  are  laudable.  =  I  /.  Some  S  is  P. 

No.  7,  E  I,  gives  EIA,  EIE,  EII,  EIO.  The  first,  second,  and  third  forms,  EIA, 
E1E,  EII,  violate  Rule  4th.  The  fourth,  EIO,  is  valid,  standing  the  test  of  the 
Canon.  The  valid  mood  is  known  among  logicians  by  the  mnemonic  word, 
Ferio.  It  is  illustrated  as  follows : 
g-  No  virtue  is  reprehensible ;  =  E  No  M  is  P ; 

Some  habits  are  virtues ;  =  I        Some  S  is  M ; 

fe  .-.  Some  habits  are  not  reprehensible.    =  O  .*.  Some  S  is  not  P.       x--^-K  P 

No.  8,  A  O,  gives  AOA,  AOE,  AOI,  AGO,  none  of  which  are  valid,  since  the 
negative  minor  premise,  O,  violates  the  Canon. 

The  valid  moods  in  Figure  I.  are  Barbara,  Celarent,  Darii,  Ferio. 
The  Figure  is  naturally  and  unconsciously  used,  according  to  Lambert, 
to  prove  qualities.  It  follows  from  the  "  Dictum  de  omni  et  nullo." 

2.  Figure  II,  is  that  which  has  the  middle  term  as  the 
predicate  of  both  premises.  There  follows,  from  the  result- 
ing relations  of  the  terms, — 

Canon  2d. — In  Figure  II.  the  requirements  are : 
f  Major  prem.  universal,  to  avoid  illicit  process  of  maj.  term; 
1  One  prem.  negative,  to  avoid  undistributed  middle. 

Testing  by  this  Canon  the  eight  possible  combinations  left  by  the 
General  Rules,  only  six  syllogistic  forms  are  found  valid  in  Figure 
II. :  EAE,  EAO,  AEE,  AEO,  EIO,  AOO.  These  are  reducible  to  four, 
since  EAO  and  AEO  are  but  cases  of  particular  conclusions,  included 
in  the  universals,  EAE  and  AEE. 

Leaving  the  student  to  test  the  various  possible  forms,  it  will  be  suf- 
ficient to  illustrate  the  valid  moods  by  examples.  The  moods  are 
known  among  logicians  as  Cesare,  Camestres,  Festino,  Baroko. 

S      Nothing  material  has  free  will  ;  =  E       No  P  is  M ;         HP  J 

g      All  spirits  have  free  will ;  =A       AllSisM;         ^~^l 

<->  .-.  No  spirit  is  material.  =  E    .-.  No  S  is  P.  V  f   S 

M  ^^i=rf 

Cesare  is  a  valid  mood,  as  is  seen  by  its  conforming  to  the  Canon,  in  its  uni- 
versal negative  major  premise,  E. 


I 


THE    UNFOLDING    OF   REASONING.        173 


All  colors  are  visible ;  =  A       All  P  is  M ; 
No  sound  is  visible ;      =  E       No  S  is  M ; 
/.  No  sound  is  a  color.      =  E       No  S  is  P. 


Camestres  is  a  valid  mood,  since  it  conforms  to  the  Canon  in  its  universal 
major  premise,  A,  and  negative  minor,  E. 

S      No  vice  is  praiseworthy;  =E       NoPisM; 

g      Some  actions  are  praiseworthy ;    =  I        Some  S  is  M ; 

fa  .-.  Some  actions  are  not  vices.  =  O  /.  Some  S  is  not  P.    VLV    M 

Festino  is  a  valid  mood,  since  it  conforms  to  the  Canon  in  its  universal  neg- 
ative major  premise,  E. 

5      All  birds  are  oviparous ;  =A      AllPisM; 

Jj      Some  animals  are  not  oviparous ;  =  O       Some  S  is  not  M . 

m  .*.  Some  animals  are  not  birds.          =  O  /.  Some  S  is  not  P. 

*r 

Baroko  is  a  valid  mood,  since  it  conforms  to  the  Canon  in  its  universal  major 
premise  and  negative  minor. 

Figure  II.  is  naturally  and  unconsciously  used,  according  to  Lambert, 
to  prove  di/erences.  It  follows  from  a  "Dictum  de  diverse:"  "Things 
which  are  different  do  not  belong  to  each  other." 

3.  Figure  III.  is  that  which  has  the  middle  term  as  the 
subject  of  both  premises.  There  follows,  from  the  resulting 
relations  of  the  terms, — 

Canon  3d. — In  Figure  III.  the  requirements  are : 
(  Minor  prem.  affirmative  to  avoid  illicit  process  of  maj.  term; 
\  Conclusion  particular  to  avoid  illicit  process  of  min.  term. 

Testing  by  this  Canon  the  eight  combinations  of  premises,  six  are 
found  to  be  valid  in  this  Figure:  AAI,  IAI,  All,  EAO,  OAO, 
EIO.  These  are  known  among  logicians  as  Darapti,  Disamis, 
Datisi,  Felapton,  Bokardo  (Dokamok),  Ferison. 

M 

a      All  gilding  is  metallic ;  =A       AllMisP; 

«g      All  gilding  shines ;  =  A       All  M  is  S ; 

Q  /.  Some  things  that  shine  are  metallic.  =  I   .'.  Some  S  is  P. 

Darapti  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor  premise,  A,  and  its  particular  conclusion,  I. 

en 

'g      Some  acts  of  homicide  are  laudable ;  =  I       Some  M  is  P 
3      All  acts  of  homicide  are  cruel ;  =  A      All  M  is  S ; 

Q  /.  Some  cruel  acts  are  laudable.  =  I  /.  Some  S  is  P. 

*          15* 


174  PRACTICAL    LOGIC. 

Disamis  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor  premise,  A,  and  its  particular  conclusion,  I. 

!»       All  acts  of  homicide  are  cruel ;     "      =  A     All  M  is  P ; 
^       Some  acts  of  homicide  are  laudable ;  =  I      Some  M  is  S ; 
/.  Some  laudable  acts  are  cruel.  =  I  .-.  Some  S  is  P. 

CO 

Datisi  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor,  I,  and  its  particular  conclusion,  I. 

c" 

Q 

*£       No  material  substance  is  a  moral  subject;      =E    NoMisP; 
.2        All  material  substance  is  extended;  =  A    All  M  is  S; 

fit  .'.  Some  extended  thing  is  not  a  moral  subject.  =  O/.  Some  S  is  not  P. 

Felapton  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor  premise,  A,  and  its  particular  conclusion,  O. 

d 

"2       Some  syllogisms  are  not  regular ;  =  O     Some  M  is  not  P 

J4       All  syllogisms  are  things  important ;       =  A     All  M  is  S ; 
ffl  .'.  Some  important  things  are  not  regular.  =  O .'.  Some  S  is  not  P. 

Bokardo  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor  premise,  A,  and  its  particular  conclusion,  O. 

JNo  truth  is  without  result ;  =  E     No  M  is  P : 

Some  truths  are  misunderstood ;  =  I      Some  M  is  S ; 
£  .'.  Some  things  misunderstood  are 

not  without  result.  =  O  /.  Some  S  is  not  P. 

Ferison  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  affirmative 
minor  premise,  I,  and  its  particular  conclusion,  O. 

Figure  III.  is  naturally  and  unconsciously  used,  according  to  Lam- 
bert, to  prove  examples  and  conceptions  (concepts  proper).  He  founds 
it  on  a  "  Dictum  de  exemplo :"  "  When  one  finds  things  A  which  are  B, 
then  there  are  A  which  are  B." 

4.  Figure  IV.  is  that  which  has  the  middle  term  as  the 
predicate  of  the  major  premise  and  the  subject  of  the 
minor.  There  follows,  from  the  resulting  relations  of  the 
terms, — 

Canon  4th. — In  Figure  IV.  the  requirements  are : 
C  If  either  prem.  neg.,  maj.  prem.  universal  to  avoid  illic.  major; 
<  If  maj.  prem.  affirm.,  min.  prem.  universal  to  avoid  undistrib.  mid. ; 
(  If  min.  prem.  affirm.,  conclusion  particular  to  avoid  illicit  minor. 
Testing  by  this  Canon  the  eight  combinations  of  premises,  five  are  found  to 
be  valid  in  this  Figure :  AAI,  AEE,  IAI,  EAO,  EIO.    These  are  known  among 
logicians  as  Bram-antip,  Camenes,  Dimaris,  Fesapo,  Fresison. 


THE    UNFOLDING    OF  REASONING. 


175 


All  greyhounds  are  dogs ;  =  A     All  P  is  M ; 

All  dogs  are  quadrupeds ;  =  A     All  M  is  S ; 

Some  quadrupeds  are  greyhounds.  =  I  /.  Some  S  is  P. 


Bramantip  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  universal 
minor  premise,  A,  with  particular  conclusion,  I. 


All  ruminating  animals  have  four 

stomachs ;  =  A  All  P  is  M  ; 

No  animal  with  four  stomachs  is 

carnivorous ;  =  E  No  M  is  S ; 

No  carnivorous  animal  ruminates.  =  E  .'.  No  S  is  P. 


Camenes  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  universal 
major  premise,  A,  and  its  universal  minor  premise,  E. 


Some  practically  virtuous  men  are 

necessarians ;  —  I      Some  P  is  M  ; 

•~      All  necessarians  speculatively  sub- 
vert the  distinction  of  vice  and 
2  virtue;  =A     AllMisS; 

.-.  Some  who  speculatively   subvert 
"          the  distinction  of  vice  and  vir- 
tue are  practically  virtuous.         =  I  /.  Some  S  is  P. 

Dimaris  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  universal 
minor  premise,  A,  and  its  particular  conclusion,  I. 


No  negro  is  a  Hindoo ;  =  E  No  P  is  M ; 
All  Hindoos  are  blacks ;  -  A  All  M  is  S ; 
Some  blacks  are  not  ne- 


groes. 


=  0  /.  Some  S  is  not  P. 


Fesapo  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  universal  major 
premise,  E,  its  universal  minor  premise,  A,  and  its  particular  conclusion,  O. 

No  moral  principle  is  an 

animal  impulse ;  =  E      No  P  is  M ; 

•55      Some  animal  impulses  are 

principles  of  action ;        =  I      Some  M  is  S ; 
^  /.  Some  principles  of  action 
10          are  not  moral  principles.  =  O  .'.  Some  S  is  not  P. 

Fresison  is  a  valid  mood,  since  it  conforms  to  the  Canon,  in  its  universal 
major  premise,  E,  and  in  its  particular  conclusion,  O. 

Figure  IV.  is  the  reverse  of  Figure  I.  It  is  naturally  and  uncon- 
sciously used,  according  to  Lambert,  to  prove  reciprocities.  He  founds 
it  on  a  "  Dictum  de  reciproco  :"  "  If  no  M  is  B,  no  B  is  this  or  that  M  ; 
if  C  is  or  is  not  this  or  that  B,  there  are  B  which  are  or  are  not  C." 


176  PRACTICAL    LOGIC. 

IV.  Collected  Results. 

For  convenient  reference  the  results  of  the  testing  of  the 

o 

various  forms  may  be  gathered  up  and  tabulated. 
1.  Table  of  Moods,  Valid  and  Invalid. 


•5i 
*§, 

£X 

Conclu. 

Moods. 

Tested. 

•s?| 

»§, 

=  i 
S| 

Conclu. 

Moods. 

Tested. 

A 

A 

E 

I 

0 

AAA 

AAE 
A  AI 

A  AO 

V.  C.  i. 

I.  C.  2.  3.  4. 
I.  P.  1. 

y.c.2i(W).3.4. 

L  R  I. 

A 

A 

E 

I 
O 

E  A  A 
EAE 

E  AI 
EAO 

I.  P.  2. 

V.  C.  I.  2. 

I.  C.  3.  4. 
I.  P.  2. 
V.cC.2(W,3.4. 

E 

A 

E 

I 
0 

AE  A 
AEE 

AEI 
ABO 

I.  P.  2. 
V.  C.  2.  4. 
I.  C.  1.  3. 
I.  P.  2. 
V.C.2(W>4.(W). 
I.  C.  1.  3. 

E 

A 
E 

I 
0 

EEA 

EEE 

EEI 
EEO 

I.  P.  3.  R.  5. 
I.  P.  3.  R.  5. 

I.  P.  3.  R.  5. 
I.  P.  3.  R.  5. 

A 

V, 

AIA 
AI  E 

I.  R.  4. 
I  P  1  R  4 

A 
F 

El  A 
E  I  E 

I.  P.  2.  R.  4. 
I  R  4 

I 

I 
O 

All 
AIO 

V.  C.  i.  3. 
I.  C.  2.  4. 
I.  P.  1. 

I 

I 
O 

EH 
EIO 

I.  P.  2. 
V.  C.  i.  2.  3.  4- 

A 

V, 

AO  A 
AO  E 

I.  P.  2.  R.  4. 
I.  R.  4. 

A 

F, 

EGA 
EOE 

I.  P.  3.  R.  4. 
.  P.  3.  R.  4.  5. 

O 

I 
O 

AOI 
AGO 

I.  P.  2. 
V.  C.  2. 

I.  C.  1.  3.  4. 

O 

I 
0 

EOI 
EOO 

.  P.  3.  R.  5. 
.  P.  3.  R.  5. 

A 

A 

E 
I 

O 

I  A  A 
IAE 
I  AI 

IAO 

I.  R.  4. 
I.  P.  1.  R.  4. 
V.  C.  3.  4- 
I.  C.  1.  2. 
I.  P.  1. 

A 

A 

E 
I 
O 

O  A  A 
O  A  E 
OAI 
OAO 

.  P.  2.  R.  4. 
.R.4. 
.P.  2. 
V.  C.  3. 
.  C.  1.  2.  4. 

E 

A 
E 

I 
O 

I  EA 
IEE 
IEI 
IEO 

I.  P.  2.  R.  4. 
I.  R.  4. 
I.  P.  2. 
I.  R.  7. 

E 

A 
E 
I 
O 

OE  A 
OEE 
OEI 
OEO 

P.  3.  R.  4.  5. 
P.  3.  R.  4.  5. 
.  P.  3.  R.  5. 
.P.3.  R.4.5. 

A 

F 

IIA 
HE 

I.  P.  3.  R.  6. 
I.  P.  1.  3.  R.  4.  6. 

A 

F 

OIA 
O1E 

.  P.  2.  3.  R.  4.  6. 
.  P.  3.  R.  6. 

1 

I 
O 

III 
HO 

I.  P.  3.  R.  6. 
I.  P.  1.  3.  R.  6. 

I 

I 
O 

Oil 
OIO 

P.  2.  3.  R.  4.  6. 
P.  3.  R.  6. 

A 

F 

IO  A 
I  O  E 

I.  P.  2.  3.  R.  4.  5. 
I  P  3  R  4.  6. 

A 
F 

OO  A 
OOE 

P.  3.  R.  4.  5.  6. 
P.  3.  R.  4.  5.  6. 

O 

I 
O 

101 
IOO 

I.  P.  2.  3.  R.  4.  6. 
I.  P.  3.  R.  6. 

O 

I 
O 

001 
OOO 

P.  3.  R.  4.  5.  6. 
P.  3.  R.  4.  5.  6. 

Note.— In  the  column  headed  "Tested,"  V  denotes  valid;  I,  invalid;  P, 
principle;  R,  rule;  C, both  canon  and  figure;  W,  weak  (indicating  a  partic- 
ular conclusion  where  a  universal  might  be  drawn).  The  student  will  find 
profitable  exercise  in  applying  the  tests  to  all  the  forms  and  figures. 


THE    UNFOLDING    OF   REASONING. 


177 


2.  Things  Proved  by  the  Figures. 


Fig.     Proved. 
I.  Attribute. 


II.  Difference. 


III.  Example. 


IV.  Eeoiprocity. 


Process. 

Ascribes  to  the  thing  what  we 
know  of  its  attribute.  It  con- 
cludes from  the  genus  to  the 
species. 

Leads  to  the  discrimination  of 
things,  and  relieves  perplex- 
ity in  our  notions.  Affords 
only  negative  conclusions. 

Affords  examples  and  excep- 
tions in  propositions  which 
appear  general.  Gives  only 
particular  conclusions. 

Finds  species  in  a  genus  in  Bra- 
mantip  and  Dimaris;  shows 
that  the  species  does  not  ex- 
haust the  genus  in  Fesapo 
and  Fresison ;  denies  of  the 
species  what  was  denied  of 
the  genus  in  Camenes. 


Dictum. 

Dictum  de  Omni  et 
Nullo.  What  is 
true  of  all  A  is 
true  of  every  A. 

Dictum  de  Diverso. 
Things  which  are 
different  are  not 
attributes  of  each 
other. 

Dictum  de  Exem- 
plo.  When  we  find 
things  A  which 
are  B,  in  that  case 
some  A  are  B. 

Dictum  de  Recip- 
roco.  If  no  M  is  B, 
no  B  is  this  or  that 
M ;  if  C  is  (or  is 
not)thisorthatB, 
there  are  B  which 
are  (or  are  not)  C. 


3.  Valid  Moods  in  the  Four  Figures. 

The  valid  moods  in  all  the  Figures  have  been  embodied  in  five  Latin 
hexameter  lines : 

Fig.  1.  Barbara,  Celarent,  Darii,  Ferio^we  prioris; 
Fig.  2.  Cesare,  Camestres,  Festino,  Baroko  (or  Fakofo),  secundce; 
Fig.  3.   Tertia  Darapti,  Disamis,  Datisi,  Felapton, 

Dokamok  (Bokardo),  Ferison   habet.     Quarto,  insuper  addit 
Fig.  4.  Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

V.  Reduction  of  Figures. 

Figure  I.  has  been  looked  upon  by  logicians  as  the  normal  Figure, 
to  which  all  the  others  may  be  reduced.  The  object  of  Logical  Reduc- 
tion is  to  bring  arguments  of  the  last  three  Figures  into  the  form  of 
Figure  I.,  and  thus  bring  all  alike  to  the  test  of  Aristotle's  Dictum.  It 
is  thus  shown  that  this  Dictum,  which  is  clearly  the  regulating  prin- 
ciple in  Figure  I.,  is  also  the  regulating  principle  in  all  deductive  rea- 

M 


178  PRACTICAL    LOGIC. 

soning,  and  that  the  process  is,  therefore,  always  substantially  the 
same  (p.  138). 

Note.— Reduction  is  usually  described  as  being  of  two  kinds:  Direct  or  Os- 
tensive,  and  Indirect  (Eeductio  ad  impossibUe).  The  latter  method  was  the  re- 
sult of  a  mistaken  notion  of  the  logicians  that  Baroco  and  Bocardo  could  not 
be  directly  reduced,  and  is  of  no  value  theoretical  or  practical.  Fakofo  and 
Dokamok  will  be  substituted  for  Baroco  and  Bokardo,  and  may  be  reduced 
by  the  direct  method. 

The  mnemonic  words  in  the  last  three  Figures  were  designed  to  in- 
dicate not  only  the  mood  of  syllogisms,  but  also  the  principles  by  which 
they  are  to  be  reduced.  The  valid  forms  in  the  four  Figures  must  be 
kept  in  view  in  reduction. 

The  initial  consonant,  B,  C,  D  or  F,  in  the  last  three  Figures  indi- 
cates the  mood  in  the  first  Figure  to  which  the  syllogism  reduces. 
Thus,  a  syllogism  in  the  mood  Cesare,  Fig.  II.,  reduces  to  Celarent. 

The  inserted  consonants,  s,  p,  k,  f,  m,  indicate  the  various  processes 
in  reduction.  S  indicates  that  the  proposition  symbolized  by  the  vowel 
preceding  it  is  to  be  converted  simply  (p.  127);  p,  by  limitation  or  per 
accidens  (p.  127) ;  k,  by  contraposition  (p.  128) ;  f,  by  infinitation  or 
obversion  (p.  124).  The  letter  m  (mutari)  indicates  that  the  premises 
of  the  given  syllogism  are  to  be  transposed.  The  p  in  Bramantip 
shows  that,  after  converting  simply,  the  premises  warrant  a  universal 
conclusion. 

The  other  consonants,  b,  d,  1,  n,  r,  t,  a,re  not  significant,  but  are  in- 
serted for  the  sake  of  euphony,  or  of  the  metre  in  the  mnemonic  hex- 
ameters invented,  to  keep  the  moods  and  figures  in  mind,  by  Petrus 
Hispanus,  who  died  in  1277  as  Pope  John  XXII. 

The  process  of  reduction  may  be  illustrated  by  the  following  examples: 
Figure  II.  Figure  I. 

NoPisM;  f     NoMisP; 

Cesare  =  ^      All  S  is  M ;  Celarent  =  \      All  S  is  M ; 

No  S.  is  P.  I  .-.  No  S  is  P. 


Bashfulness  is  not  something  thor- 
oughly good ; 

Modesty  is  something  thoroughly 

good; 
/.  Modesty  is  not  bashfulness. 


Nothing  thoroughly  good  is  bash- 
fulness  ; 

Modesty  is  something  thoroughly 
good; 

Modesty  is  not  bashfulness. 


The  C  in  Cesare  indicates  that  the  mood  reduces  to  Celarent ;  the  s,  that  the 
major  premise  is  to  be  converted  simply. 

Figure  III.  Figure  I. 

AllMisP;  C      AllMisP; 

Darapti  =  -|      AllMisS;  Darii  =  j      Some  S  is  M; 

,  Some  S  is  P.  (.  /.  Some  S  is  P, 


THE    UNFOLDING    OF  REASONING. 


179 


All  whales  are  mammalia ; 
All  whales  are  water  animals ; 
Some  mammalia  are  water  animals. 


All  whales  are  mammalia ; 
Some  water  animals  are  whales ; 
.'.  Some  mammalia  are  water  animals. 


The  D  in  Darapti  indicates  that  the  mood  reduces  to  Darii ;  the  p,  that  the 
preceding  proposition,  A,  is  to  be  converted  by  limitation. 

Note.— The  student  can  readily  carry  the  work  of  reduction  through  all  the 
figures  and  moods. 

Topic  Third. — Complex  and  Abnormal  Forms. 

In  books  and  in  conversation  arguments  usually  appear 
in  incomplete  or  irregular  forms,  and  often  combined  as 
polysyllogisms  manifest  or  occult.  In  dealing  with  these, 
the  incomplete  forms,  except  in  the  case  of  such  regular 
forms  as  the  Sorites,  need  to  be  completed  and  the  irreg- 
ular forms  reduced  to  regularity.  The  general  rules  then 
become  applicable. 

The  greater  part  of  this  work  the  student  may  be  left  to  carry  out 
for  himself  by  aid  of  the  principles  already  laid  down.  There  is  need, 
however,  to  present  the  principles  which  govern  the  Sorites,  to  con- 
sider briefly  some  peculiar  forms  of  argumentation,  and  to  exhibit 
especially  the  calculation  of  probabilities. 

I.  The  Sorites  Tested. 

The  Sorites,  or  chain  of  Enthymemes  in  Fig.  I.,  has  al- 
ready been  denned  and  illustrated  (p.  143).  There  are  two 
ways  of  testing  the  Sorites :  by  completing  all  the  abridged 
syllogisms  (p.  144),  and  then  applying  the  usual  tests ;  or  by 
using  a  system  of  rules  which  may  be  immediately  applied. 
The  former  method  may  be  left  to  the  student  himself ;  only 
the  latter  needs  to  be  illustrated. 

From  the  nature  of  the  Sorites  the  following  principles  result : 

1.  The  first  proposition  furnishes  the  major  premise  of  the  first  com- 
pleted syllogism  ;  the  last  proposition  is  the  conclusion  of  the  last  syl- 
logism and  of  the  whole  chain  ;  the  intermediate  propositions  are  the 
minor  premises  of  the  successive  syllogisms.     The  number  of  syllogisms 
must,  therefore,  equal  the  number  of  minor  premises. 

2.  The  major  premise  of  each  successive  syllogism  after  the  first  is 
furnished  by  the  conclusion  of  the  preceding  syllogism. 

The  reasoning  must  conform  to  the  Canon  of  Fig.  I. 


180  PRACTICAL    LOGIC. 

Rule  1st. — Every  major  premise  must  be  universal  in  order  to  avoid 
undistributed  middle.  It  follows  that  only  the  last  proposition  in  the 
progressive  sorites  and  the  first  in  the  regressive  may  be  particular,  since 
any  other  particular  premise  would  result  in  making  the  conclusion 
of  its  syllogism,  or  the  next  major  premise,  particular  also. 

Kule  2d. — Every  minor  premise  must  be  affirmative  in  order  to 
avoid  illicit  process  of  the  major  term.  It  follows  that  only  one 
premise  may  be  negative,  the  last  proposition  in  the  regressive  sorites 
and  the  first  in  the  progressive,  since  these  only  are  not  minor  premises. 

The  Sorites  and  its  Rules  may  be  illustrated  by  the  following  examples, 
which  are  abridged  to  admit  of  compact  parallel  statement : 


Regressive  Sorites. 
Some  prosperous  are  avaricious ; 
The  avaricious  are  intent  on  gain ; 
The  intent  on  gain  are  discontented ; 
The  discontented  are  not  happy  ; 
.*.  Some  prosperous  are  not  happy. 


Progressive  Sorites. 

No  discontented  are  happy; 
All  intent  on  gain  are  discontented ; 
All  avaricious  are  intent  on  gain ; 
Some  prosperous  are  avaricious ; 
,  Some  prosperous  are  not  happy. 


It  has  been  often  asserted  that  Sorites  cannot  occur  in  any  other  than  Fig.  I. 
It  has  been  shown,  however,  by  Mill,  that  one  step,  and  only  one,  step  in  a  So- 
rites may  be  either  in  Figure  II.  or  Figure  III. 

II.  Peculiar  Forms  of  Argumentation. 

The  usual  form  of  direct  proof  of  propositions  is  known 
among  logicians  as  the  argumentum  ad  rem,  or  proof  of  the 
thing  itself.  As  variations  from  it  or  in  contrast  with  it  may 
be  noted  the  argumentum  a  fortiori,  the  argumentum  adjudi- 
cium,  the  argumentum  ad  populum,  the  argumentum  ad 
verecundiam,  the  argumentum  ad  ignorantiam,  the  argumen- 
tum ad  homincm,  and  the  reductw  ad  absurdum. 

The  argumentum  a  fortiori,  or,  "  by  a  stronger  reason,"  is  one  involving  com- 
parative judgments.  It  is  based  upon  the  maxim,  "  What  is  greater  than  a 
greater  is  greater  still  than  the  thing."  The  argument  is  essentially  mathe- 
matical or  quantitative.  Thus : 

Asia  is  larger  than  Africa ; 
Africa  is  larger  than  Europe ; 
.*.  By  much  more  is  Asia  larger  than  Europe. 
This  may  also  be  presented  as  follows : 

The  Atlantic  Ocean  is  as  large  as  Lake  Superior  (and  more) ; 
Lake  Superior  is  as  large  as  the  Dead  Sea  (and  more) ; 
.'.  The  Atlantic  Ocean  is  as  large  as  the  Dead  Sea  (and  still  more). 
The  argument  a  fortiori  is  also  denned  as  "  the  proof  of  a  conclusion  deduced 
from  that  of  a  less  probable  supposition  that  depends  upon  it."    For  example, 
see  Matthew  vi.  30  and  vii.  11. 


THE  UNFOLDING  OF  REASONING.    181 

The  argumentum  ad  judicium  is  based  upon  the  common  judgments  of  man- 
kind. Its  maxim  is,  "  What  all  men  everywhere  and  always  believe,  is  true," 
or  the  so-called  principle  of  common  sense  on  which  the  Scottish  philosophy 
of  Reid  rests.  The  argument  has  great  force  when  it  is  really  based  on  the 
common  judgment  of  mankind.  The  danger  of  appealing  to  this  principle 
without  sufficient  grounds  is,  however,  very  great.  Under  the  confident  asser- 
tions, "  Everybody  says,"  "  No  one  pretends  to  think,"  the  greatest  fallacies 
are  often  covered.  The  argument  may  be  illustrated  as  follows : 

The  material  world  is  a  reality  and  our  perception  of  it  immediate,  because 
all  men,  everywhere  and  always,  have  so  believed. 

The  argumentum  ad  populum  is  based  on  an  appeal  to  public  opinion,  or  to 
passion  or  prejudice,  rather  than  intelligence.  It  is  often  employed  because 
no  really  good  arguments  are  to  be  found,  or  because  it  is  easier  to  appeal  to 
the  passions  and  prejudices  of  the  masses  than  to  their  intelligence.  It  often 
puts  forward  as  its  major  premise  the  false  maxim,  "  Vox  popuM  Vox  Dei," 
"  The  voice  of  the  people  is  the  voice  of  God." 

The  argumentum  ad  verecundiam  is  an  appeal  to  the  feelings  of  reverence 
for  certain  persons  or  objects,  instead  of  proceeding  to  prove  the  point  in  hand. 
The  Scholastics  used  as  a  standing  major  premise  the  maxim,  "  It  is  foolish  to 
affirm  that  Aristotle  erred." 

The  argumentum  ad  ignorantiam  is  addressed  to  the  ignorance  of  men.  It 
sometimes  consists  in  assuming  that  a  position  is  correct  because  an  adversary 
cannot  show  the  contrary ;  sometimes,  in  taking  advantage  of  men's  ignorance 
to  impose  upon  them  by  some  shallow  sophism,  false  statement,  or  confident 
assertion. 

Under  this  may  be  included  the  Fallacy  of  Interrogation,  in  which  a  question 
is  so  put  as  to  be  equivalent  to  a  confident  assertion  of  some  error.  The  de- 
mand for  an  adequate  conception  (p.  91)  or  description,  often  made  by  a  brow- 
beating lawyer  upon  a  witness  in  court,  is  of  the  same  character.  It  is  only  a 
few  experts  who  can  give  anything  more  than  a  clear  notion  (p.  91)  of  the 
handwriting,  features,  or  dress  of  the  most  intimate  friend. 

The  argumentum  ad  hominem  is  an  appeal  to  the  practice,  principles  or 
professions  of  an  opponent  as  confirming  our  own  position  or  destructive  to 
his.  An  opponent  may  thus  be  silenced,  since  the  argument  is  good  against 
him,  even  though  it  be  not  good  against  the  views  he  advocates.  As  soon  as  he 
renounces  such  practice,  principles  or  professions,  the  argument  ceases  to  be 
of  value  as  against  him.  Our  Lord  often  used  this  method  to  silence  the  cavils 
of  the  Jews ;  for  example,  Matthew  xxii.  41-45. 

The  reductio  ad  absurdum  proves  a  proposition  indirectly  by  proving  the 
absurdity  of  its  contradictory.  It  has  already  been  considered  (p.  129). 

III.  Calculation  of  Probabilities. 

The  theory  of  probabilities,  or  of  chances,  as  it  is  some- 
times designated,  has  in  recent  times  received  increased 
attention.  In  an  elementary  work  there  is  only  space  for 
the  simplest  rules  and  cases. 

Thomson  has  described  chance  as  "  the  amount  of  belief  with  which  we 
expect  one  or  other,  out  of  two  or  more  uncertain  events."     Uncertain, 
16 


182  PRACTICAL    LOGIC. 

or  merely  probable,  events  are  "  those  wherein  no  cause  or  law  appears 
to  determine  the  occurrence  of  one  rather  than  another."  Jevons  pro- 
poses "  to  dispense  altogether  with  this  obscure  word  '  belief,'  and  to 
say  that  the  theory  of  probability  deals  with  quantity  of  knowledge." 
An  event  is  merely  "probable  when  our  knowledge  of  it  is  diluted 
with  ignorance,  and  exact  calculation  is  needed  to  discriminate  how 
much  we  do  and  do  not  know." 

At  the  basis  of  the  rules  for  the  calculation  of  probabilities  are  the  common- 
sense  principles  which  underlie  all  reasoning.  "  We  must  treat  equals  equally, 
and  what  we  know  of  one  case  may  be  affirmed  of  every  case  resembling  it  in 
the  necessary  circumstances.  The  theory  consists  in  putting  similar  cases  on 
a  par,  and  distributing  equally  among  them  whatever  knowledge  we  possess. 
Throw  a  penny  into  the  air,  and  consider  what  we  know  with  regard  to  its 
way  of  falling.  We  know  that  it  will  certainly  fall  upon  a  side,  so  that  either 
head  or  tail  will  be  uppermost;  but  as  to  whether  it  will  be  head  or  tail,  our 
knowledge  is  equally  divided.  Whatever  we  know  concerning  head,  we  know 
also  concerning  tail,  so  that  we  have  no  reason  for  expecting  one  more  than 
the  other.  The  least  predominance  of  belief  to  either  side  would  be  irra- 
tional ;  it  would  consist  in  treating  unequally  things  of  wkich  our  knowledge 
is  equal." 

The  Rules  concern  either  simjda  9r  combined  probabilities. 

Bale  1st.  —  A  single  probability  of  any  uncertain  event  is  ascer- 
tained by  dividing  the  number  of  chances  favorable  to  the  event  by 
the  total  number  of  chances  favorable  and  unfavorable. 

Thus  the  probability  that  the  head  will  fall  uppermost,  when  a  penny  is 
thrown  into  the  air,  is  expressed  by  ^.  The  probability  that  a  man  blind- 
folded will  draw  a  white  ball  out  of  an  urn  containing  2  white  balls  and  8 
black  ones  is  expressed  by  ^  or  £.  To  take  a  different  case,  if  the  letters  of  the 
word  Roma  are  thrown  down  casually  in  a  row.  what  is  the  probability  that 
they  will  form  a  significant  Latin  word  ?  The  possible  combinations  of  the 
four  letters  are  4  X  3  X  2  X  1  =  24.  If  all  the  combinations  are  examined,  7  will 
be  found  to  have  a  meaning,  namely,  Roma,  ramo,  oram,  mora,  maro,  armo,  and 
amor.  Hence  the  probability  sought  is  &. 

Bule  2d.  —  The  probability  of  the  independent  recurrence  of  an 
event  is  found  by  multiplying  together  the  fractions  expressing  the 
single  probabilities. 

Thus  the  probability  of  throwing  head  twice  with  a  penny  is  %  X  %  =  % : 
the  probability  of  throwing  it  three  times  is  yz  X  Yz  X  Yz  =  Y&  This  Rule  will 
be  seen  to  rest  on  Rule  1st,  since  the  denominator  represents  the  possible  com- 
b' nations  in  the  case,  or  the  whole  number  of  ways  of  the  happening  of  the 
compound  event,  and  the  numerator  the  number  of  ways  favorable. 

Bule  3d.  — "  In  order  to  calculate  the  probability  that  an  event  al- 
ready observed  will  be  repeated  any  given  number  of  times,  divide 
the  number  of  times  the  event  has  been  observed,  increased  by  one, 


TEE    UNFOLDING    OF   REASONING.         183 

by  the  same  number  increased  by  one  and  the  number  of  times  the 
event  is  to  recur." 

"  Thus,  if  the  tide  had  been  observed  9  times,  the  chance  that  it  would  recur 
10  times  more  would  be  f  +  j  0  +j  =  ^  —  J.  This  is  the  same  thinS  as  if 
each  reproduction  of  the  observed  event  corresponded  to  putting  a  white  ball 
in  an  urn  where  there  were  already,  before  commencing  the  trials,  a  white 
ball  and  as  many  black  balls  as  it  is  supposed  that  the  event  observed  should 
re-occur  times." 

Two  or  more  probabilities  if  mutually  dependent  weaken  each  other, 
while  if  independent  they  strengthen  each  other. 

Eule  4th.  —  In  case  of  mutually  dependent  probabilities,  or  prob- 
abilities of  probabilities,  the  total  probability  is  reached  by  multiply- 
ing together  the  several  single  probabilities. 

Thus,  if  the  credibility  (p.  105)  of  a  witness  be  %,  and  his  competency  (p. 
104),  or  ability  to  know  the  facts  of  which  he  testifies,  be  %,  the  total  probabil- 
ity of  his  telling  the  truth  is  %  X  %  =  §  =  Y&  As  certainty  is  represented  by 
unity,  the  testimony  will,  in  this  case,  be  twice  as  likely  to  be  false  as  it  is  to 
be  true. 

Kule  5th.  —  In  case  of  independent  probabilities  the  total  probabil- 
ity is  reached  by  subtracting  each  separate  probability  from  unity 
(which  gives  the  probability  of  the  opposite  event,  in  each  case,  or  the 
probability  of  a  probability),  multiplying  the  separate  results  together 
(according  to  Rule  4th),  and  subtracting  this  product  from  unity 
(thus  arriving  at  the  probability  of  the  original  compound  event). 

Thus,  the  total  probability  that  the  Gospels  are  true  may  be  made  up  from 
the  probability  arising  from  the  character  of  the  authors,  represented  by  % . 
from  the  absence  of  any  motive  on  the  part  of  the  authors  to  fabricate  such 
accounts,  represented  by  % ;  from  the  influence  of  the  Gospels  themselves 
upon  the  world,  represented  by  $.  Subtracting  each  of  these  from  unity  and 
multiplying  the  results  together,  we  have,  as  the  probability  of  imposture, 
1A  X  VA  X  \  =  sV  This  subtracted  from  unity  gives  fg  as  the  probability  of  the 
truth  of  the  Gospels. 

Note. —  See  Thomson's  Laws  of  Thought;  Jevon's  Principles  of  Science;  New- 
comb's  Algebra. 

Praxis.  —  In  the  following  syllogisms  show  whether  the  premises 
are  true.  Name  the  middle,  minor,  and  major  terms.  Name  the  mood 
and  figure  of  each,  showing  whether  valid  or  not.  Reduce  any  mood 
in  the  other  Figures  to  Fig.  I.  Bring  out  the  relation  of  reason  and 
consequent  involved  in  connection  with  the  middle  term  in  each  case, 
substituting  the  letters,  S,  P,  M,  for  the  terms  in  the  general  formula, 
and  giving  the  relation  of  the  notions  by  the  circular  notation. 

1.  No  human  weakness  can  belong  to  God  ;  some  attributes  imputed 


184  PRACTICAL   LOGIC. 

to  the  Deity  by  mythology  are  human  weaknesses ;  hence  (at  least) 
some  attributes  imputed  to  the  Deity  by  mythology  cannot  belong  to 
Him. 

2.  Some  who  act  in  accordance  with  law  do  not  do  what  is  right 
with  right  intention ;  .*.  some  who  act  legally  are  not  morally  disposed. 

3.  Every  real,  natural  poem  is  naive ;  those  poems  of  Ossian  which 
Macpherson  pretended  to  discover  are  not  naive  (but  sentimental) ; 
hence  they  are  not  real,  natural  poems. 

4.  The  sum  total  of  the  worlds  belonging  to  our  solar  system  must 
completely  determine  the  orbit  of  Uranus ;  the  known  worlds  of  our 
solar  system  do  not  fully  account  for  the  orbit  of  Uranus ;  hence  the 
whole  of  the  worlds  of  our  so.lar  system  are  not  known. 

5.  Passive  mental  states  make  men  neither  noble  nor  base,  worthy 
of  praise  or  of  blame ;  the  virtues  do  this ;  .*.  the  virtues  are  not  pass- 
ive mental  states. 

6.  All  squares  are  rectilineal  plane  figures ;   some  parallelograms 
are  squares ;  /.  some  parallelograms  are  rectilineal  plane  figures. 

7.  No  form  of  knowledge,  which  corresponds  to  a  peculiar  form  of 
existence,  is  of  merely  didactic  value ;  syllogism  is  a  form  of  knowledge 
which  corresponds  to  a  peculiar  form  of  existence  (viz.,  to  the  real  con- 
formability  to  law) ;  hence  the  syllogism  is  not  of  mere  didactic  worth. 

8.  All  cetaceous  animals  are  water  animals ;  all  cetaceous  animals 
are  mammalia ;  hence  some  mammalia  are  water  animals. 

9.  Some  persons  accused  of  witchcraft  have  not  believed  themselves 
to  be  free  from  the  guilt  laid  to  their  charge ;  all  those  accused  of 
witchcraft  were  accused  of  a  merely  feigned  crime ;  hence  some  who 
were  accused  of  a  merely  feigned  crime  have  not  believed  themselves 
free  from  the  guilt  laid  to  their  charge. 

10.  Jubeo  is  not  a  verb  sentiendi  vel  declarandi ;  jubeo  takes  the  con- 
struction of  the  accusative  and  infinitive ;  hence  at  least  one  or  some 
Latin  verbs  which  take  the  construction  of  accusative  and  infinitive 
are  not  verbs  sentiendi  vel  declarandi. 

11.  All  squares  are  regular  figures  ;  some  parallelograms  are  squares  ; 
.•.  some  parallelograms  are  regular  figures. 

12.  Some  parallelograms  are  squares  ;  all  squares  are  regular  figures; 
.*.  some  regular  figures  are  parallelograms. 

13.  All  squares  are  parallelograms ;  no  parallelogram  has  converg- 
ing opposite  sides ;  .*.  no  square  has  converging  opposite  sides. 

14.  Good  non-conductors  of  heat  retain  heat  longer  ;  woollen  clothes 
are  good  non-conductors ;  .'.  woollen  clothes  retain  "heat  longer. 

15    Some  things  which  retain  heat  longer  are  woollen  clothes ;  things 


THE    UNFOLDING    OF  REASONING.         185 

which  retain  heat  longer  are  good  non-conductors ;  .'.  woollen  clothes 
are  good  non-conductors. 

Supply  the  conclusions  to  each  of  the  following  pairs  of  premises, 
and  show  whether  the  conclusion  is  valid,  or  why  no  conclusion  can 
be  drawn.  Treat  the  syllogisms  as  required  in  the  preceding  examples. 

1.  All  good  reasoners  are  candid ;   some  infidels  are  not  candid ; 


2.  The  ox,  deer,  sheep,  goat,  etc.,  are  ruminant ;  the  ox,  the  deer, 
etc.,  are  as  good  as  all  horned  animals ;  .• 

3.  Oaks  are  vegetables ;  oysters  are  not  oaks ;  .• 

4.  No  good  action  results  in  evil ;  some  alms-giving  results  in  evil ; 


5.  Animals  are  bodies  having  organization  and  sensation;   frogs 
have  organization  and  sensation  ;  / 

6.  Some  of  our  tax  laws  are  oppressive  measures;  all  oppressive 
measures  should  be  repealed ;  .• 

7.  Reptiles  bring  forth  their  young  by  eggs ;  the  rat  does  not  bring 
forth  its  young  by  eggs ;  / 

8.  The  connection  of  soul  and  body  is  to  be  believed ;  the  connec- 
tion of  soul  and  body  is  incomprehensible ;  / 

9.  True  poets  are  men  of  genius ;   very  unwise  men  have  proved 
true  poets ;  .* 

10.  All  good  men  are  sincere ;  Rousseau  was  sincere ;  .• 

11.  Political   Economy   is    a    profitable    study ;    profitable   study 
sharpens  the  intellect ;  .* 

12.  No  truth  is  worthless  ;  many  truths  are  misapplied ;   / 

13.  Most  people  are  careless ;  most  people  are  destitute  of  perfect 
health;  / 

14.  90  out  of  every  100  men  are  imprudent ;  90  out  of  every  100 
are  unsuccessful ;  .*.     .     '.     .     .     . 

15.  Elephants  are  stronger  than  horses ;  horses  are  stronger  than 
men ;  / 

Section  II,— Unfolding  of  the  Hypothetical  Syllogism, 
Hypothetical  syllogisms  have  already  been  defined  and 
divided  (pp.  144-146).    They  will  now  be  considered  in  the 
order  of  the  division  given. 

Topic  First  — The  Conditional  or  Conjunctive  Syllogism. 

The  conditional  syllogism  may  either  be  tested  as  it  is, 


186  PRACTICAL    LOGIC. 

or  reduced  to  categorical  form  and  then  tested  by  the  prin- 
ciples of  categorical  reasoning. 

I.  The  Tests  of  Conditional  Syllogisms. 

The  tests  of  conditional  syllogisms  arise  out  of  their  na- 
ture as  directly  embodying  the  principle  of  Reason  and 
Consequent.  From  this  it  follows  that,  if  the  reason  be 
present  in  any  given  case  we  may  be  sure  of  the  presence 
of  the  consequent ;  and  if  the  consequent  be  absent  we  may 
be  sure  of  the  absence  of  its  reason.  Hence  the  two  forms 
of  conditionals,  the  constructive  and  destructive,  and  the 
Rules  applicable  to  these  forms  of  reasoning. 

Bale  1st.  —  Affirming  the  antecedent  or  reason  affirms  the  conse- 
quent (modus  ponens] ;  while  denying  the  consequent  denies  the  ante- 
cedent (modus  tollens). 

The  first  part  of  the  Rule  gives  the  constructive  conditional,  which 
affirms  the  reason  or  antecedent,  and  then  on  the  ground  of  this  af- 
firms the  consequent.  The  second  part  gives  the  destructive  condi- 
tional, which  denies  the  consequent,  and  on  the  ground  of  this  denies 
the  reason.  The  two  forms  may  be  illustrated  as  follows : 

.£  Antecedent.  Consequent. 

3       If  General  Grant  has  a  fever,          he  is  sick ;  Major  premise. 

•g       He  has  a  fever ;  (Modus  ponens).  Minor  premise. 

o  •'.  He  is  sick.  Conclusion. 

o 

Antecedent.  Consequent. 

3       If  General  Grant  has  a  fever,  he  is  sick ;  Major  premise. 

*j       He  is  not  sick;  (Modus  tollens.)  Minor  premise. 

Q  /.  He  has  not  a  fever.  Conclusion. 

The  absence  of  the  particular  reason  or  antecedent  mentioned  in  any 
given  case  does  not  render  certain  the  absence  of  the  consequent,  since 
antecedents  or  reasons  are  manifold  and  the  consequent  may  follow 
from  other  antecedents.  So  the  presence  of  the  consequent  does  not 
argue  the  presence  of  a  particular  antecedent  or  reason,  since  it  may 
be  the  consequent  or  effect  of  some  other  antecedent.  Hence 

Rule  2d.  —  Denying  the  antecedent  does  not  deny  the  consequent; 
and  affirming  the  consequent  does  not  affirm  the  antecedent. 


THE  UNFOLDING  OF  REASONING.    187 

Antecedent.  Consequent. 

{If  there  is  fire  in  the  stove ;  the  room  will  be  warm ;  Major  premise. 

There  is  no  fire  in  the  stove ;  (Deny  Ant.)  Minor  premise. 

.• No  conclusion. 

If  there  is  fire  in  the  stove ;  the  room  will  be  warm ;  Major  premise. 

The  room  is  warm.  (Affirm  Conseq.)  Minor  premise. 

.• No  conclusion. 

In  the  case  of  the  denial  of  the  antecedent  the  conclusion  that  the 
room  will  not  be  warm  does  not  follow,  since  it  may  be  warmed  by  a 
grate,  or  a  furnace,  or  steam  apparatus,  or  a  warm  sun  in  summer,  or 
the  presence  of  a  large  audience,  or  by  being  on  fire,  etc.  In  the  case 
of  the  affirmation  of  the  consequent,  the  particular  antecedent  does 
not  follow,  since  the  same  thing  may  result  from  any  one  of  the  ante- 
cedents enumerated. 

The  whole  may  be  illustrated  by  diagram : 


®         Furnace.  ~~      -- —        '~^~^ 

Heated    % 
3         Steam. 

I  ••  £pa 

_*5b_  Room.    I 


The  dotted  lines  may  represent  the  possible  lines  of  reason  or  causa- 
tion ;  the  heated  room,  the  consequent  or  effect.  If  the  stove  is  pres- 
ent, then  the  heated  room  will  be  present,  because  that  is  a  sufficient 
reason.  If  the  stove  is  not  present,  the  room  may  still  be  heated,  since 
the  grate,  furnace,  etc.,  may  furnish  the  sufficient  reason.  If  there  is 
not  the  heated  room,  then  all  the  antecedents  must  be  absent, — stove,  etc. 
If  there  be  the  heated  room,  no  definite  a  priori  conclusion  concerning 
the  agency  of  the  stove  is  possible,  since  the  consequent  may  result 
from  any  other  of  the  antecedents. 

II,  Reduction  of  the  Conjunctive  Syllogism. 

The  conjunctive  or  conditional  syllogism  may  readily  be 
reduced  to  the  categorical  form,  as  already  shown  (p.  117), 


188  PRACTICAL    LOGIC. 

and  then  tested  by  the  Rules  which  apply  to  the  various 
Figures. 

Applying  the  principles  of  reduction  to  the  syllogism  just  given,  it 
becomes : 

i  st.  The  case  of  the  presence  of  the  heated  stove  is  the  case  of  a  warm  room ; 

The  present  is  the  case  of  a  heated  stove ; 
M*  .'.  The  present  is  the  case  of  a  warm  room. 

gj  Or  A. :      Every  room  in  which  a  stove  is  heated  is  warm ; 
£        A.        This  is  a  room  in  which  a  stove  is  heated ; 
A.   .*.  This  room  is  a  warm  room. 

£  2d.  A.      Every  room  in  which  the  stove  is  heated  is  warm ; 

3         E.       This  room  is  not  warm ; 

•£        E.   /.  The  stove  is  not  heated  in  this  room. 

£»  3d.  A.      Every  room  in  which  the  stove  is  heated  is  warm ; 

E.       This  is  a  room  in  which  the  stove  is  not  heated ; 
.5«        E.   .'.  This  room  is  not  warm.    (Not  valid.) 
M 

This  form  corresponding  to  the  denial  of  the  antecedent,  under  Rule  2d,  in- 
volves illicit  process  of  the  major  term. 

u  4th.  A.      Every  room  in  which  the  stove  is  heated  is  a  warm  room ; 

3          A.       This  room  is  a  warm  room ; 

•S?         A.  .*.  This  room  is  one  in  which  the  stove  is  heated.    (Not  valid.) 

This  form  corresponding  to  the  affirming  of  the  consequent,  under  Rule  2d, 
involves  undistributed  middle,  or  substantially  four  terms. 

Topic  Second. — The  Disjunctive  Syllogism. 

The  tests  of  the  disjunctive  syllogism  arise  out  of  the  na- 
ture of  the  disjunctive  judgment,  as  embodying  the  prin- 
ciple of  Excluded  Middle,  in  connection  with  Reason  and 
Consequent  the  principle  of  all  reasoning. 

A  perfect  disjunctive  judgment  embodies  a  complete  division  of  some 
genus  or  class,  and  the  alternatives  presented  are  the  species  under 
that  class,  and  are  reciprocally  exclusive  (p.  71). 

The  major  premise  presents  these  species  as  alternatives. 

The  minor  premise  makes  a  categorical  predication  concerning  one 
or  other  of  the  species  or  alternatives. 

The  conclusion  draws  an  inference  concerning  the  other  species. 

Kule  1st. — See  that  the  disjunction  exhausts  the  division,  and  that 
the  disjunctives  are  reciprocally  exclusive. 

Kule  2d. — Affirming  a  part  of  the  disjunctives,  wholly  or  disjunc- 
tively, in  the  minor  premise,  denies  all  the  others  in  the  conclusion. 


THE  UNFOLDING  OF  REASONING.    189 

Rule  3d. — Denying  a  part  of  the  disjunctives,  in  the  minor  prem- 
ise, affirms  the  rest,  in  the  conclusion,  wholly  or  disjunctively,  ac- 
cording as  one  or  more  may  remain. 

These  may  be  illustrated  by  the  following  examples : 

The  Apostles  must  have  been  fanatics,  or  impostors,  or  true  men; 

They  were  neither  fanatics  nor  impostors ; 

.*.  They  were  true  men. 

The  season  of  the  battle  of  Lexington  must  have  been  spring,  or  summer,  or 

autumn,  or  winter ; 
It  was  neither  summer  nor  winter ; 
/.  It  was  either  autumn  or  spring. 

In  the  first  example  the  character  of  the  Apostles  is  analyzed  into 
three  possible  exclusive  phases,  and  we  affirm  that  if  they  do  not  be- 
long to  one  or  other  of  the  first  two  they  must  belong  to  the  third.  In 
the  second  example  the  seasons  are  analyzed  into  the  four,  and  we  af- 
firm that  since  it  was  neither  the  second  nor  fourth  it  was  one  of  the 
other  two. 

Topic  Third. — The  Dilemmatic  Syllogism. 

The  dilemma  tic,  or  conjunctive-disjunctive,  syllogism  is 
subject  to  the  Rules  of  conditionals  and  disjunctives.  The 
most  common  forms  are  the  following : 

I.  One  Antecedent  in  the  Major  with  Disjunctive  Consequent. 

This  takes  the  form :  If  A  is  B,  either  C  is  D  or  E  is  F.  By  the 
rules  of  conditionals  and  disjunctives  we  have  the  following  possible 
cases  and  results : 

Affirm  Antecedent.  A  is  B ;  /.  either  C  is  D  or  E  is  F. 

Deny  Cons,  wholly.  Neither  C  is  D  nor  E  F ;  /.  A  is  not  B. 

Deny  Cons,  disjunctively.      Either  C  is  not  D  or  E  is  not  F.    No  conclusion. 

Denial  of  Antecedent.  A  is  not  B.  No  conclusion. 

Affirmation  of  Consequent.  C  is  D  or  E  is  F  No  conclusion. 

II.  Plurality  of  Antecedents  in  the  Major  with  Common  Consequent. 

This  takes  the  form :  If  A  is  B,  X  is  Y,  and  if  C  is  D,  X  is  Y.  This 
gives  the  following  oases  and  results : 

Affirm  Antec.  wholly.  A  is  B  and  C  is  D ;  .-.  X  is  Y. 

Affirm  Antec.  disjunct.  A  is  B  or  C  is  D ;  .'.X  is  Y. 

Deny  Consequent.  X  is  not  Y ;  .'.  neither  A  is  B  nor  C  is  D. 

Deny  Antecedents.  A  is  not  B  nor  is  C  D.    No  conclusion. 

Affirm  Consequent.  X  is  Y.  No  conclusion. 

III.  Plurality  of  Antecedents  in  Major,  each  with  its  own  Conse- 
quent. 


190  PRACTICAL    LOGIC. 

This  takes  the  form :  If  A  is  B,  C  is  D,  and  if  E  is  F,  G  is  H.  This 
gives  the  following  oases  and  results : 

Affirm  Ant.  wholly.     A  is  B  and  E  is  F ;  /.  C  is  D  and  G  is  H, 

Affirm  Ant.  di&junct.  A  is  B  or  E  is  F ;  .'.  C  is  D  or  G  is  H. 

Deny  Cons,  wholly.     C  is  not  D  and  C  is  not  H ;  /.A  is  not  B  and  E  is  not  F. 

Deny  Cons,  disjunct.  C  is  not  D  and  G  is  not  H ;  /.A  is  not  B  or  E  is  not  F. 

Deny  Antecedent.       A  is  not  B  and  E  is  not  F.    No  conclusion. 

Affirm  Consequent.     C  is  D  and  G  is  H.  No  conclusion. 

Note.— All  the  forms  enumerated  are  called  dilemmatic  syllogisms,  but.  as 
already  stated  (p.  146),  the  dilemma,  in  the  strict  sense,  is  only  that  form  which 
has  a  plurality  of  antecedents  in  the  major,  and  a  disjunctive  minor.  This 
dilemma  is  sometimes  rebutted  by  another  with  an  opposite  conclusion.  Aris- 
totle illustrates  the  process  of  rebuttal  thus :  "  An  Athenian  mother  said  to  her 
son, '  Do  not  engage  in  public  affairs ;  for  if  you  do  what  is  just  men  will  hate 
you,  and  if  you  do  what  is  unjust  the  gods  will  hate  you.'  This  the  son  re- 
butted by  the  following  retort :  '  I  ought  to  enter  into  public  affairs ;  for  if  I  do 
what  is  unjust  men  will  love  me,  and  if  I  do  what  is  just  the  gods  will  love 
me.' " 

Praxis. — In  the  following  examples,  complete  the  syllogisms  if  in- 
complete. Name  the  kind  in  each  case  and  formulate  with  letters  and 
illustrate  by  diagram.  Test  each  example  by  the  Rules. 

1.  If  men  are  virtuous  they  are  wise,  and  if  they  are  vicious  they 

are  unwise ; 

But  they  are  either  virtuous  or  vicious ; 
/.  They  are  either  wise  or  unwise. 

2.  If  the  classics  teach  how  to  produce  wealth  they  ought  to  be 

studied ; 

They  do  not  so  teach ; 
/.  They  ought  not  to  be  studied. 

3.  Mahomet  was  either  an  enthusiast  or  an  impostor; 
He  was  an  enthusiast ; 

/.  He  was  not  an  impostor. 

4.  If  there  be  no  future  life,  then  either  virtue  receives  its  due  re- 
ward in  the  present  world,  or  there  is  no  perfect  government  admin- 
istered over  men  ;  neither  of  which  is  admissible. 

5.  The  fact  that  I  defended  him  is  a  proof  that  I  hold  him  innocent. 

6.  If  pain  is  severe,  it  will  be  brief;  and  if  it  last  long,  it  will  be 
slight ;  hence  it  should  be  borne  patiently. 

7.  If  this  man  were  wise,  he  would  not  speak  irreverently  of  Scrip- 
ture in  jest,  and  if  he  were  good,  he  would  not  do  so  in  earnest ; 

But  he  does  it  either  in  jest  or  in  earnest; 


THE   UNFOLDING    OF  REASONING.         191 

Section  III.— Conspectus  of  Fallacies, 

A  fallacy  is  any  unsound  or  delusive  mode  of  reasoning. 
The  principal  fallacies  in  induction  and  deduction  need  to  be 
particularized  and  distinguished. 

In  order  to  acquire  a  complete  command  of  the  principles  of  reason- 
ing and  to  guard  against  error,  the  thinker  must  make  himself  familiar 
with  the  most  common  kinds  of  fallacy.  In  the  previous  Sections,  as 
Jevons  has  said,  "  we  have  considered,  as  it  were,  how  to  find  the  right 
road ;  it  is  our  task  here  to  ascertain  the  turnings  at  which  we  are 
most  liable  to  take  the  wrong  road." 

Note.— With  respect  to  the  knowledge  or  intention  of  the  reasoner,  fallacies 
have  been  divided  into  paralogisms  and  sophisms.  A  paralogism  is  a  fallacy 
which  is  unknown  to  the  reasoner  himself;  a  sophism  is  a  false  argument,  un- 
derstood to  be  so  by  the  reasoner  himself  and  intentionally  used  to  deceive. 
This  is  not,  however,  a  logical  distinction,  since  it  is  not  based  upon  the  thought, 
but  upon  the  mental  and  moral  condition  of  the  reasoner,  and  is,  therefore,  of 
no  logical  value. 

Topic  First. — Fallacies  in  Induction. 

In  induction  we  deal  with  matters  of  fact.     The  require- 
ments of  induction  are  summed  up  in  two  things : 
1st.  Exact  Observation  of  the  facts. 
2cL  Correct  Interpretation  of  the  facts. 

All  fallacies  in  induction  arise  from  failure  to  conform  to 
these  requirements. 

I.  Fallacies  from  Failures  in  Exact  Observation. 

1.  Neglect  of  observation,  or  ignoring  of  all  facts  (pp.  26-34,  148, 
155). 

2.  Partial  observation,  giving  incomplete  view  of  the  facts  (pp.  33, 
148,  155). 

3.  Neglect  of  exceptional,  and  especially  contradictory,  facts  (p.  155). 

4.  Assuming  what  is  not  fact  to  be  fact  (pp.  33,  148). 

5.  Mixing  illegitimate  inferences  with  the  facts  (p.  33). 

II.  Fallacies  from  Failures  in  Correct  Interpretation. 

1.  Neglect  of  all  cause,  or  confounding  induction  with  mere  general- 
ization (pp.  147,  153),  including  groundless  universal  conclusion  from 
few  unimportant  facts  (fictce  universalitatis)  (p.  159). 

2.  Partial  explanation  of  the  facts,  by  assuming  an  improper  or  in- 
sufficient cause,  including: 


192  PRACTICAL    LOGIC. 

(1.)  Assuming  inappropriate  cause  (p.  154). 

(2.)  Assuming  inadequate  cause  (p.  154). 

(3.)  Assuming  a  single  cause  where  there  is  a  complex  of  causes  (p.  154). 

3.  Neglect  of  real  cause  for  hypothetical  cause  (p.  154). 

4.  Fallacy  of  unreal  reason,  or  assuming  what  is  not  a  cause  to  be  a 
cause  (non  causa  pro  causa)  (p.  160),  including: 

(1.)  Confounding  antecedent  and  cause  (post  hoc  ergo  propter  hoc)  (p.  149). 

(2.)  Confounding  concomitant,  condition  or  occasion  and  cause  (cum  hoc  ergo 
propter  hoc)  (p.  149). 

(3.)  Confounding  law  and  cause  (p.  149). 

Note.— The  most  noted  forms  of  the  fallacy  of  unreal  reason  are  the  lazy 
reason  (ignava  ratio),  the  reaper  (ratio  mctens),  and  the  controlling  reason  (ratio 
dominans).  These  are  all  of  the  same  character,  and  may  be  illustrated  by  an 
example  of  the  first,  which  gave  it  its  name : 

Sumption.—"  If  I  ought  to  exert  myself  to  effect  a  certain  event,  this  event 
either  must  take  place  or  it  must  not; 

Sub-sumption. — "  If  it  must  take  place,  my  exertion  is  superfluous;  if  it  must 
not  take  place,  my  exertion  is  of  no  avail ; 

Conclusion. — "  Therefore,  on  either  alternative,  my  exertion  is  useless." 

In  regard  to  the  vice  of  this  sophism,  Krug,  as  quoted  by  Hamilton,  says: 
11  It  is  manifest  that  it  lies  in  the  sumption,  in  which  the  disjunct  members  are 
imperfectly  enounced.  It  ought  to  have  been  thus  conceived :  If  I  ought  to 
exert  myself  to  effect  a  certain  event,  which  I  cannot,  however,  of  myself 
effect,  this  event  must  either  take  place  from  other  causes,  or  it  must  not  take 
place  at  all.  It  is  only  under  such  a  condition  that  my  exertion  can,  on  either 
alternative,  be  useless,  and  not  if  the  event  depend  wholly  or  in  part  for  its 
accomplishment  on  my  exertion  itself,  as  the  conditio  sine  qua  non." 

This  shows  that  this  so-called  syllogism  formally  violates  Rule  1st  under 
disjunctives  (p.  188),  as  applied  to  the  dilemma. 

5.  Assuming  unverified  hypotheses  as  truth  (pp.  156,  160). 

Topic  Second. — Fallacies  in  Deduction  or  Syllogism. 

Deductive  reasoning  deals  with  truths  or  general  princi- 
ples. Its  requirements  are,  therefore,  summed  up  in  two 
things : 

1st.  Correct  Matter  or  Thought,  or  the  grasping  of  true 
premises. 

2d.  Correct  Form  in  Reasoning,  or  the  proper  unfolding 
of  what  is  contained  in  the  premises. 

All  fallacies  in  deduction  result,  therefore,  from  failure  to  comply 
with  one  or  both  these  requirements.  Those  which  result  from  some 
failure  in  the  matter  or  thought  are  known  as  Material  Fallacies ; 
those  resulting  from  some  failure  in  the  form  of  reasoning  are  known 


THE    UNFOLDING    OF   REASONING.        193 

as  Logical  or  Formal  Fallacies ;  those  resulting  from  failure  in  both 
matter  and  form  are  known  as  Semi-Logical  Fallacies. 

I.  Material  Fallacies. 

Material  fallacies  are  those  which  arise  outside  of  the 
mere  form  of  thought,  or  verbal  statement  (extra  dictionem), 
in  the  subject-matter  or  thought  itself.  They  may  take  the 
form  of  unwarranted  assumption  of  premises,  or  of  irrelevant 
conclusion  from  the  proper  premises. 

1.  Unwarranted  Assumption  of  Premises. 

(1.)  Begging  the  question  (petitio  principii),  or  virtual  assumption 
of  the  thing  to  be  proved  or  of  that  by  which  it  is  to  be  proved.  This 
includes : 

a.  Petitio  principii  proper,  where  the  assumption  is  openly  made  without 
show  of  proof. 

b.  Arguing  in  a  circle,  where  the  conclusion  is  virtually  used  to  prove  the 
premise. 

E.  g.,  John  Knox  and  John  Witherspoon  are  excellent  men  because  they  be- 
longed to  an  excellent  church,  the  Presbyterian  Church ;  and  the  Presbyterian 
Church  is  an  excellent  one  because  it  has  contained  such  good  men. 

c.  Assuming  a  resemblance  without  proving  it,  or  where  there  is  no  such 
resemblance  (non  tale  pro  tali). 

E.  g., «'  All  other  religions  are  delusions ;  therefore,  Christianity  is  a  delusion." 

(2.)  Failure  in  Estimating  Probabilities. 

a.  Over-estimation  of  dependent  probabilities  (p.  182). 

b.  Under-estimation  of  independent  probabilities  (pp.  108, 188). 

2.  Irrelevant  Conclusion  from  Proper  Premises. 

(1.)  Fallacy  from  arguing  to  the  wrong  point.  This  is  also  called 
ignoratio  elenchi,  or  "  ignoring  the  refutation,"  which  refutation  in- 
volves the  establishment  of  the  contradictory  (p.  129).  This  includes: 

a.  Perverted  argument  from  common  consent  (argumentum  ad  judicium) 
(p.  181). 

b.  Argumentum  ad  populum  (p.  181). 

c.  Argumentum  ad  verecundiam  (p.  181). 

d.  Argumentum  ad  ignorantiam  (p.  181). 

e.  Argumentum  ad  hominem  (p.  181). 

(2.)  Fallacy  from  simple  Confusion  of  Thought.     This  includes: 

a.  Fallacy  of  accident  (fallacia  accidentis)  and  the  converse  (p.  167).  This 
includes : 

(a.)  Arguing  from  a  general  rule  to  a  special  case,  where  some  accidental  cir- 
cumstance renders  the  rule  inapplicable. 

(b.)  Arguing  from  a  special  case  to  a  general  one.  This  is  described  by  the 
17  N 


194  PRACTICAL   LOGIC. 

Latin  phrase,  "  a  dicto  secundum  quid  ad  dictum  simpliciter,"  meaning  "  from  a 
statement  under  a  condition  to.  a  statement  simply  or  without  that  condition." 
(c.)  Arguing  from  one  special  case  to  another  special  case. 

b.  Fallacy  of  the  consequent,  or  non  sequitur,  where  the  reasoning  is  so  loose 
and  inconsequent  that  no  one  can  discover  any  force  in  it. 

c.  Fallacy  of  many  questions  (plures  interrogationum),  which  results  from  so 
combining  two  or  more  questions  that  no  true  answer  can  be  given  to  them. 

II.  Logical  or  Formal  Fallacies. 

Logical  fallacies  are  those  which  occur  in  the  mere  form 
of  the  statement  (in  dictione) .  They  may  ordinarily  be  dis- 
covered by  the  aid  of  the  rules  of  deduction  or  the  syllo- 
gism, without  any  knowledge  of  the  subject-matter  of  the 
argument.  They  are  violations  of  the  Rules  of  Reasoning 
categorical  and  hypothetical. 

1.  Fallacies  in  Categorical  Reasoning. 

(1.)  Violation  of  the  Rules  for  Terms. 

a.  Four  Terms  (quaternio  terminorum).    Breach  of  Rule  1st  (p.  166). 

b.  Undistributed  Middle.    Breach  of  Rule  2d  (p.  167). 

c.  Illicit  Process  of  Major  or  Minor.    Breach  of  Rule  3d  (p.  167). 

(2.)  Violation  of  the  Rules  for  Premises. 

a.  Failure  of  conclusion  to  follow  weaker  part.    Breach  of  Rule  4th  (p.  168). 

b.  Conclusion  from  two  negative  premises.    Breach  of  Rule  5th  (p.  168). 

c.  Conclusion  from  particular  premises.    Breach  of  Rule  6th  (p.  168). 

d.  Conclusion  from  particular  major  with  negative  minor.    Breach  of  Rule 
7th  (p.  170). 

2.  Fallacies  in  Hypothetical  Reasoning. 

(1.)  Violation  of  Rules  for  Conditionals. 

Conclusion  from  denying  antecedent  or  from  affirming  consequent. 
Breach  of  Rule  2d  (p.  186). 

(2.)  Violation  of  Rules  for  Disjunctives. 

a.  Confounding  partitive  and  disjunctive  judgments  (p.  118). 

b.  Disjunctive  elements  not  exclusive  and  inclusive.    Breach  of  Rule  1st 
(p.  188). 

c.  Conclusion  not  in  accordance  with  the  affirmation  or  denial  of  disjunction. 
Breach  of  Rules  2d  and  3d  (pp.  188, 189). 

III.  Semi-Logical  Fallacies. 

Semi-logical  fallacies  are  fallacies  partly  material  and 
partly  formal. 

These  fallacies  arise  largely  from  the  ambiguous  use  of  terms.  In 
such  cases  the  term  used  in  two  senses  is  substantially  equivalent  to 


THE    UNFOLDING    OF  REASONING.        195 

two  terms.  The  ambiguity  must  first  be  detected  by  examining  into 
the  meaning  of  the  terms.  The  fallacy  is  so  far  material.  When  the 
ambiguity  is  fairly  detected,  the  fallacy  is  at  once  transformed  into  the 
formal  or  logical  fallacy  of  four  terms.  It  includes : 

1.  Fallacy  of  Equivocation,  consisting  in  the  use  of  the 

same  word  in  two  distinct  senses. 
(1.)  Fallacy  of  ambiguous  middle  (p.  82). 
(2.)  Fallacy  of  homonymous  terms  (p.  83). 

2.  Fallacy  of  Amphibology,  consisting  in  ambiguous  gram- 
matical structure  of  a  sentence. 

E.  g.,  "  The  Duke  yet  lives  that  Henry  shall  depose." 

3.  Fallacy  of  Composition  and  Division,  arising  from  using 
a  term  distributively  (pp.  112, 115)  in  one  premise,  and  col- 
lectively (pp.  54,  113)  in  the  other. 

This  is  especially  common  in  the  use  of  "  all"  (p.  113),  "  not  all"  (p.  Ill),  etc. 

4.  Fallacy  of  Etymology.     This  includes : 
(1.)  Fixing  upon  a  wrong  root  (p.  76.) 

(2.)  Assuming  that  the  original  meaning  of  the  root  of  a  word  de- 
cides the  present  meaning  of  the  word  (p.  76). 

Note.— For  enumerations  of  the  sources  of  human  error,  see  Bacon's  Novum 
Organum,  Lib.  i. ;  Mill's  Logic,  Book  V.,  ch.  ii. ;  Hamilton's  Logic,  Lect.  xxiii. 

Praxis. — Examine  the  following  arguments,  completing  them  if  in- 
complete, and  reducing  to  regular  form  if  irregular.  Examine  and  de- 
fine the  important  conceptions  or  terms.  Name  the  kind  of  argument 
in  each  case,  formulating  with  letters  and  illustrating  by  diagram. 
Present  the  proof  of  the  premises.  Test  each  example  by  the  Rules, 
naming  and  explaining  the  fallacy,  material,  logical  or  semi-logical, 
wherever  such  fallacy  exists.  If  categorical,  reduce  to  Fig.  1. 

1.  A  science  which  furnishes  the  mind  with  a  multitude  of  useful 
facts  deserves  cultivation;  but  Logic  is  not  such  a  science;  .•.  Logic 
does  not  deserve  cultivation. 

2.  Nuisances  are  punishable  by  law ;  to  keep  a  noisy  dog  is  a  nui- 
sance ;  .*.  to  keep  a  noisy  dog  is  punishable  by  law. 

3.  Twice  two  and  three  are  seven;  twice  two  and  three  are  ten; 
/.  seven  is  equal  to  ten. 

4.  If  motion  is  possible,  a  body  must  move  either  in  the  place  where 
it  is,  or  in  a  place  where  it  is  not ;  but  a  body  cannot  move  in  a  place 


196  PRACTICAL   LOGIC. 

where  it  is,  and  of  course  it  cannot  move  where  it  is  not ;  /.  motion  is 
impossible. 

5.  What  you  bought  yesterday  you  eat  to-day ;  you  bought  raw 
meat  yesterday ;  /.  you  eat  raw  meat  to-day. 

6.  The  Jews  are  avaricious;  .'.  the  prophet  Daniel  was  avaricious. 

7.  All  bodies  that  move  themselves  are  animated ;  the  stars  move 
themselves ;  /.  the  stars  are  animated. 

8.  Mouse  is  a  syllable ;  but  a  mouse  eats  cheese ;  .'.  a  syllable  eats 
cheese. 

9.  If  it  be  fated  that  you  recover  from  your  present  disease,  whether 
you  call  in  a  doctor  or  not  you  will  recover ;  again,  if  it  be  fated  that 
you  do  not  recover  from  your  present  disease,  whether  you  call  in  a 
doctor  or  not  you  will  not  recover ;  But  one  or  other  of  the  contra- 
dictories is  fatal ;  .'.  To  call  in  a  doctor  is  of  no  consequence. 

10.  Episcopacy  is  of  Scripture  origin;  the  Church  of  England  is 
the  only  episcopal  church  in  England ;  .*.  the  Church  established  is 
the  Church  that  should  be  supported. 

11.  Carbon  is  combustible ;    diamonds   are  composed   of  carbon ; 
/.  diamonds  are  combustible. 

12.  Rain  has  fallen,  if  the  ground  is  wet;  but  the  ground  is  not 
wet ;  .*.  rain  has  not  fallen. 

13.  None  but  mortals  are  men ;   monarchs  are  men ;  .'.  monarchs 
are  mortals. 

14.  Logic  as  it  was  cultivated  by  the  Schoolmen  proved  a  fruitless 
study ;  .-.  Logic  as  it  is  cultivated  at  the  present  day  must  be  a  fruit- 
less study. 

15.  Men  can  live  without  animal  food,  and  they  can  live  without 
vegetable  food,  as  has  been  often  demonstrated ;  but  all  food  is  either 
animal  or  vegetable;  /.  men  can  live  without  food. 

16.  All  birds  are  animals ;  no  reptiles  are  birds ;  .*.  no  reptiles  are 
animals. 

17.  He  who  is  most  hungry  eats  most;  he  who  eats  least  is  most 
hungry ;  /.  he  who  eats  least  eats  most. 

18.  If  rain  has  fallen,  the  ground  is  wet ;  but  rain  has  not  fallen ; 
.*.  the  ground  is  not  wet. 

19.  Night  must  be  the  cause  of  day,  for  it  invariably  precedes  it. 

20.  If  Brandreth's  pills  are  of  any  value,  those  who  take  them  will 
improve  in  health ;   my  friend  who  has  been  taking  them  has   im- 
proved in  health ;  /.  they  are  of  value. 

21.  He  that  can  swim  needs  not  despair  to  fly ;  for  to  swim  is  to  fly 
in  a  grosser  fluid,  and  to  fly  is  to  swim  in  a  subtler. 


THE    UNFOLDING    OF   REASONING.        197 

22.  The  ground  is  wet,  if  rain  has  fallen;  the  ground  is  wet;  /.  rain 
has  fallen. 

23.  All  stars  are  self-luminous ;  all  planets  are  not  self-luminous ; 
/.  no  planets  are  stars. 

24.  Some  flowers  are  tulips ;  all  flowers  are  beautiful ;  /.all  the  tu- 
lips are  beautiful. 

25.  The  probability  of  the  existence  of  a  God,  derived  from  the  ex- 
istence of  the  universe,  may  be  stated  as  f ;  from  order  in  the  universe, 
f ;  from  conscience,  f ;  from  common  belief  of  mankind,  f,  etc.     These 
all  fall  far  below  unity  or  full  proof ;  .'.  the  proofs  of  the  existence  of 
a  God  are  insufficient  to  warrant  belief. 

26.  If  the  books  in  the  Alexandrine  Library  be  in  conformity  with 
the  doctrines  of  the  Koran,  there  is  no  need  of  them  ;  if  adverse,  then 
also  they  should  be  burned. 

27.  If  the  ground  is  wet,  rain  has  fallen ;  but  rain  has  fallen ;  /.  the 
ground  is  wet. 

28.  The  hope  of  immortality  is  either  a  rational  expectation  or  an 
illusion ;  but  that  belief  cannot  be  an  illusion  which  all  the  most  en- 
lightened peoples  have  adopted. 

29.  Personal  deformity  is  an  affliction  of  nature ;  disgrace  is  not  an 
affliction  of  nature ;  /.  personal  deformity  is  not  disgrace. 

30.  No  idle  person  can  be  a  successful  writer  of  history ;  .*.  Hume, 
Macaulay,  Hallam,  and  Grote  must  have  been  industrious. 

31.  Bacon  was  a  great  lawyer  and  statesman ;  and  as  he  was  also 
a  philosopher,  we  may  infer  that  any  philosopher   may  be  a  great 
lawyer  and  statesman. 

32.  Nothing  is  better  than  wisdom ;  dry  bread  is  better  than  noth- 
ing; .'.  a  fortiori  is  dry  bread  better  than  wisdom. 

33.  If  classical  education  is  worth  the  cost,  either  it  must  be  pre- 
eminently fitted  to  develop  the  mental  powers,  or  it  must  furnish  ex- 
ceedingly valuable  information ;  but  neither  alternative  can  be  main- 
tained, and  so  classical  education  is  not  worth  the  cost. 

34.  Men  love  to  be  humbugged ;  the  President  of  the  Bible  Society 
is  a  man ;  /.he  loves  to  be  humbugged. 

35.  All  power  proceeds  from  will  as  its  antecedent ;  a  steam-engine 
has  no  will ;  /.  it  has  no  power. 

36.  What  produces  intoxication  should  be  prohibited ;  the  use  of 
spirituous   liquors   produces   intoxication;    .'.  the  use   of   spirituous 
liquors  should  be  prohibited. 

37.  All  the  trees  in  the  park  make  a  thick  shade ;   this  tree  is  one 
of  them ;  .'.  this  tree  makes  a  thick  shade. 


198  PRACTICAL    LOGIC. 

38.  The  object  of  war  is  durable  peace ;    /.  soldiers  are  the  best 
peacemakers. 

39.  Improbable  events  happen  almost  every  day ;  but  what  happens 
almost  every  day  is  a  very  probable  event;  .'.  improbable  events  are 
very  probable  events. 


SUMMARY    OF    RESULTS. 

THE  aim  of  the  Logic  of  Reasoning  is,  in  general,  to  train 
to  the  best  thinking  and  fullest  appreciation  of  thought  in  its 
third  form.  The  perfection  of  thinking  as  reasoning  depends 
upon  the  degree  of  certainty  that  the  right  cause  or  mid- 
dle term  has  been  fixed  upon.  As  the  finished  result  of  Con- 
ception is  clear  and  distinct  thinking,  and  that  of  Judg- 
ment connected  thinking,  so  that  of  Reasoning  is  continuous 
thinking. 

The  conclusions  from  induction  are  probahle  truths  (judg- 
ments, p.  132),  varying  in  probability  all  the  way  from  mere 
hypotheses  to  perfected  theories.  The  conclusions  from 
deduction  are  always  certain  truths  (judgments,  p.  132) 
when  the  premises  are  certain  and  the  reasonings  correct, 
and  probable  truths  when  the  premises  are  only  probable. 

The  special  aim  of  the  Practical  Logic  of  Reasoning 
should  be  to  train  the  thinker  to  the  highest  degree  of 
skill  and  certainty  in  using  the  various  processes  of  induc- 
tion and  deduction  in  his  own  thinking,  and  to  the  greatest 
readiness  and  accuracy  in  grasping  and  testing  these  pro- 
cesses and  their  products  as  they  are  presented  in  the  think- 
ing of  others. 


PART  IV. 

THE  LOGIC  OF  CONSTRUCTION  OR  THE  SYSTEM. 


THE  aim  of  the  Logic  of  Construction  should  be  to  train 
the  student  to  skill  in  dealing  with  the  Fourth  Form  of 
Thought. 

Definition.  —  Construction  is  that  higher  form  of  thought 
in  which  we  combine  mutually  related  products  of  the  lower 
forms  of  thought,  according  to  some  rational  principle,  into 
one  relatively  complete  whole  (pp.  11-13).  The  product 
of  construction  is  known  as  the  System. 

Ueberweg  defines  system  as  "the  orderly  combination  of  mutually- 
related  knowledge  into  one  relatively  complete  whole."  System  is 
either  mechanical  or  rational.  Rational  system  is  that  in  which  the 
combination  is  a  result  of  the  application  of  some  rational  principle ; 
mechanical  system,  that  in  which  such  rational  principle  is  wanting. 

The  alphabet,  as  arranged  in  the  order,  a,  b,  c,  etc.,  is  a  mechanical 
system ;  as  arranged  in  classes,  —  as  vowels,  semi-vowels,  and  conso- 
nants; or  tonics,  subtonics,  and  atonies,  —  it  is  a  rational  system. 
There  are  three  forms  of  rational  system :  scientific  system ;  artistic 
system ;  practical  system.  These  all  imply  orderly  arrangement,  but 
they  differ  in  the  law  by  which  that  arrangement  is  effected ;  that  of 
scientific  system  being  according  to  the  law  of  the  true  ;  that  of  artistic 
system  according  to  the  law  of  the  beautiful ;  that  of  practical  system 
according  to  the  law  of  the  good. 

In  scientific  system  the  aim  is  to  combine  the  related  thoughts  in 

199 


200  PRACTICAL    LOGIC. 

such  a  way  that  the  totality  will  exactly  express  the  truth  and  the 
whole  truth.  It  is,  therefore,  said  to  be  governed  by  the  Law  of  the 
True.  In  artistic  or  aesthetic  system  the  aim  is  to  combine  the  related 
truths  in  such  a  way  as  to  produce  a  totality  which  will  express  di- 
versity in  unity,  or  beauty.  It  is,  therefore,  said  to  be  governed  by 
the  Law  of  the  Beautiful.  In  practical  system  the  aim  is  to  combine 
forces  and  agencies  as  means  so  as  to  secure  a  whole  by  which  some 
desired  end  or  good  may  be  secured.  It  is,  therefore,  said  to  be  gov- 
erned by  the  Law  of  the  Good. 

Artistic  or  aesthetic  system  belongs  to  ^Esthetics ;  the  other  forms 
may  be  regarded  as  properly  belonging  to  Logic  (p.  12),  and  will  be 
briefly  considered. 

Constructive  thinking  is  manifestly  the  highest  act  of  the 
human  intellect,  and  should,  therefore,  be  made  prominent 
in  the  later  stages  of  higher  education.  The  formation  and 
unfolding  of  systems  will  be  briefly  treated  in  successive 
Chapters. 


CHAPTER    I. 

THE  FORMATION  OP  CONSTRUCTION 
OR   SYSTEM. 

AN  understanding  of  the  combination  of  mutually  related 
thoughts  into  systems,  by  the  constructive  faculty,  must 
prepare  the  way  for  unfolding  and  testing  such  systems. 
The  process  and  the  products  will  be  considered  briefly 
under  each  of  the  forms  of  construction. 

Section  I,— Scientific  Construction. 

Scientific  construction  is  construction  according  to  the 
law  of  the  true.  Its  product  is  Scientific  System. 

Topic  First. — Process  of  Forming  and  Verifying  Scien- 
tific System. 

Three  things  are  essential  in  thinking  in  the  form  of 
scientific  system :  First,  fixing  upon  some  one  sphere  of 


THE   FORMATION    OF    CONSTRUCTION.     201 

mutually  related  thoughts,  or  thoughts  constituting  a  whole ; 
secondly,  maintaining  logical  consistency  in  the  joining  of 
all  the  parts  under  this  whole  ;  thirdly,  verifying  the  agree- 
ment of  the  resulting  combination,  in  its  parts  and  as  a 
whole,  with  the  entire  reality  of  the  sphere  which  is  being 
systematized. 

These  give  the  Laws  of  Scientific  Construction  ;  the  Laws 
of  Logical  Unity  or  Logical  Totality ;  of  Logical  Consis- 
tency ;  and  of  Logical  Truthfulness. 

I.  The  Law  of  Logical  Unity  or  Totality. 

The  unity  and  totality  of  a  system  are  determined  by 
this,  that  all  the  individual  thoughts  contained  in  it  depend 
on  a  common  principle.  A  principle,  in  this  sense,  has  been 
defined  as  "  an  absolutely  or  relatively  original  element  on 
which  a  series  of  other  elements  depends."  It  is  the  unify- 
ing thought  which  binds  together  the  otherwise  disconnected 
and  unorganized  mass  of  thoughts.  Hence  arises 

Rule  1st. — Seek  a  principle  which  will  bring  the  thoughts  to  be 
systematized  into  unity  under  one  sphere  or  whole. 

The  Law  of  Totality  may  also  be  presented  as  the  Law  of  Numer- 
ical Completeness,  which  requires  that  a  scientific  view  of  any  region 
of  fact  or  truth  shall  present  all  the  essential  facts  and  truths,  none 
added  and  none  omitted.  Any  so-called  science,  e.g.,  astronomy,  may 
be  rendered  so  far  false  by  an  addition  to  the  facts  or  truths  or  sub- 
traction from  them. 

Various  principles,  or  points  of  view,  may  be  made  use  of  in  system- 
atizing any  region  of  truth.  The  sphere  may  thus  be  enlarged  or 
diminished.  For  example,  the  astronomer  may  aim  to  present  the 
astronomy  of  the  solar  system  or  of  the  universe ;  he  may  give  his 
work  a  mathematical  or  a  descriptive  form  ;  he  may  present  the  solar 
system  and  universe  as  they  are,  or  treat  them  historically,  giving  the 
stages  in  their  development. 

II.  The  Law  of  Logical  Consistency  or  Correlation. 

The  logical  consistency  of  a  system  requires  the  proper 
joining  or  correlation  of  all  the  parts  under  the  whole  or 


202  PRACTICAL    LOGIC. 

totality.     All  the  truths  combined  should  be  in  their  proper 
relation  to  each  other. 

The  main  relations  to  be  kept  in  mind  in  such  work  are  those  of 
substance  and  properties,  as  brought  out  under  Observation  (p.  29) ; 
those  of  content  of  concepts  (p.  40)  and  extent  of  concepts  (p.  45) ; 
those  of  reason  and  consequent,  as  involved  in  induction  and  deduc- 
tion (pp.  138-9).  There  should  be  perfect  accuracy  of  thought  in  all 
the  parts  and  relations  of  the  system.  Hence  arises 

Rule  2d.  —  See  that  all  the  parts  are  properly  joined  or  articulated 
under  the  one  whole. 

Any  science,  e.  g.,  zoology,  may  be  rendered  false  by  any  departure 
from  the  facts  or  laws  of  succession  ;  or  from  the  relations  of  co-ordina- 
tion, subordination,  etc.,  brought  out  by  logical  and  scientific  division; 
or  from  the  relations  of  reason  and  consequent,  as  involved  in  induc- 
tion and  deduction. 

III.  The  Law  of  Logical  Truthfulness. 

The  logical  truthfulness  of  a  system  requires  that  the 
entire  system  so  constructed  shall,  in  all  its  parts  and  as  a 
whole,  be  in  accordance  with  the  reality,  or  the  entire 
sphere  or  whole  which  is  being  systematized.  This  con- 
formity with  the  reality  is  the  crucial  test  of  a  system. 
From  it  arises 

Rule  3d.  —  Test  the  system  of  thought  constructed  by  the  reality 
which  it  represents. 

In  any  scientific  system  any  want  of  conformity  to  the  sphere  of 
reality  renders  the  system  so  far  false.  Imaginary  schemes,  such  as 
the  scheme  of  organized  being  as  unfolded  by  Haeckel  in  his  History 
of  Natural  Evolution,  have  no  claim  to  the  name  of  scientific  system. 

Topic  Second.  —  Products  of  Scientific  Construction. 

Systems,  as  the  products  of  scientific  construction,  are 
either  absolutely  or  relatively  complete. 

Scientific  System  has  sometimes  been  confounded  with  systems  of 
classes  (p.  44),  but  it  is  manifest  that  these  merely  form  one  of  the 
elements  used  in  constructing  scientific  systems.  Science  is  used  in 
various  senses:  "exact  knowledge;"  "classified  knowledge;"  etc. 
Ueberweg  defines  it  as  a  "  whole  of  knowledge  in  the  form  of  the  sys- 


THE    FORMATION    OF    CONSTRUCTION.    203 

tern,"  in  which  sense  it  is  substantially  equivalent  to  scientific  system. 
According  to  this  view,  "  scientific  knowledge  finds  its  perfection  in 
the  combination  of  thoughts,  one  with  the  other,  into  a  whole,  which 
in  its  content  and  form  represents  the  objective  reality."  "  Science  as 
such  has  its  true  existence  only  in  the  systematic  form." 

I.  Relatively  Complete  System. 

The  Sciences,  as  we  find  them,  usually  deal  with  some 
relative  whole  and  not  with  the  entire  universe  of  truth. 
They  are  inductive,  deductive,  or  mixed,  according  to  the 
method  of  thought  employed. 

1.  The  inductive  sciences  result  from  the  employment  of  the  induc- 
tive method  of  thought. 

The  Inductive  Method  involves  three  elements : 

First,  The  scientific  investigator  starts  with  matters  of  fact. 

Secondly,  In  reaching  the  materials  for  the  science,  he  makes  use 
of  the  principles  of  inductive  reasoning  chiefly. 

Thirdly,  These  materials  are  given  their  proper  systematic  form  by 
the  principles  of  scientific  construction  (p.  201).  Its  steps  are,  as  has 
been  seen  (pp.  148-9,  200-3) :  exact  observation,  correct  interpreta- 
tion, and  scientific  construction.  The  product  is  a  system  of  thought 
wrought  out  from  the  facts. 

2.  The  deductive  sciences  result  from  the  employment  of  the  deduc- 
tive method  of  thought. 

The  Deductive  Method  involves  three  elements : 

First,  The  scientific  investigator  starts  with  ideas  or  relations  of 
ideas. 

Secondly,  In  gathering  the  materials  for  the  science  he  makes  use 
of  the  principles  of  deduction  chiefly. 

Thirdly,  These  materials  are  given  their  proper  systematic  form  by 
the  same  general  principles  of  scientific  construction  made  use  of  in 
the  inductive  method. 

Its  steps  are,  therefore  :  proper  grasp  of  truth,  or  right  judgments  or 
general  principles ;  correct  unfolding  of  truth ;  and  scientific  construc- 
tion of  the  results. 

In  it  induction  may  be  used  in  subordination  whenever  matters  of 
fact  are  incidentally  taken  into  account. 

The  product  is  a  system  of  thought  unfolded  from  fundamental 
thoughts  or  truths. 


2(M  PRACTICAL    LOO  I C. 

3.  The  mixed  sciences  arise  from  the  joint  employment  of  the  in- 
ductive and  deductive  methods.  This  results  from  the  presence  of 
both  facts  and  truths,  both  of  which  need  to  be  wrought  into  the  sys- 
tem. Astronomy  furnishes  an  illustration  of  mixed  scientific  method. 

II.  Absolutely  Complete  System. 

The  absolutely  complete  science  deals  with  all  things,  or 
the  universe.  It  aims  to  construct  the  universal  scientific 
system  and  the  universal  philosophy,  both  of  which  are  in- 
cluded under  complete  scientific  system  in  the  wide  sense. 

Herbert  Spencer  distinguishes  between  knowledge,  science,  and  phil- 
osophy as  follows :  "  Knowledge  of  the  lowest  kind  is  ununified  knowl- 
edge ;  science  is  partially  unified  knowledge ;  philosophy  is  completely 
unified  knowledge."  The  distinction  usually  made  between  science 
and  philosophy  is  as  follows :  science  deals  with  facts  and  their  order, 
or  with  the  "  what;"  philosophy  deals  with  general  principles  and  rea- 
sons, or  the  "  why."  It  is  impossible,  however,  to  have  any  science  so 
completely  empirical  as  not  to  involve  more  or  less  of  the  principles 
or  reasons  of  things,  and  equally  impossible  to  have  any  philosophy 
so  entirely  transcendental  as  not  to  embrace  a  solid  basis  of  fact  or 
reality.  In  the  highest  sense  science,  as  scientific  system,  embraces 
both  facts  and  their  reasons,  both  the  "what"  and  "the  why,"  or 
both  science  proper  and  philosophy. 

1.  The  Complete  Science. — Great  thinkers  have  sought  to 
construct  the  one  universal  scientific  system,  and  with  va- 
rious success.  The  system  of  Comte  may  be  presented  as 
one  of  the  best. 

Comte  starts  with  the  suggestion  of  Descartes,  that  "  sound  knowledge 
should  advance  from  the  simpler  to  the  more  complex  phenomena."  In 
this  suggestion  "-lay  the  germ  of  a  sound  arrangement  of  the  sciences, 
which  scarcely,  however,  seems  to  have  begun  to  bear  fruit  before  the 
time  of  Ampere  and  Comte."  Thomson,  in  his  Laws  of  Thought,  pp. 
316-319,  has  presented  the  system  drawn  from  Comte  in  brief  form. 

«'  Mathematics,  or  the  science  of  quantity,  is  at  once  the  most  simple  in  its 
elements  and  the  most  general  in  its  application,  entering  more  or  less  into  all 
the  sciences  of  nature,  and  constituting  almost  the  whole  of  that  which  comes 
next  it  in  the  order  of  dependence.  Astronomy,  or  the  science  of  the  heav- 
enly bodies,  is  the  application  of  mathematical  truths  to  the  laws  of  matter 
and  motion,  matter  and  the  motions  of  material  bodies  being  the  new  concep- 


THE  FORMATION    OF    CONSTRUCTION.     205 

tion  which  belongs  to  this  science.  Physics,  being  the  science,  or  rather  group 
of  sciences,  which  is  conversant  with  the  general  laws  of  the  world  so  far  as 
they  relate  to  beings  without  life  or  organization,  would  come  next ;  and  it 
imports,  in  addition  to  the  conceptions  of  Astronomy,  those  of  light,  of  heat, 
of  sound,  of  electricity,  of  magnetism,  and  many  others.  Chemistry  would 
rank  next,  which  is  the  science  of  the  decomposition  and  combinations  of 
the  various  substances  that  compose  and  surround  the  earth.  Next  in  order 
of  complexity  would  rank  Physiology,  founded  on  the  additional  conception 
of  vegetable  and  animal  life.  To  this  would  succeed  Anthropology,  or  the 
science  of  man's  nature ;  and  to  this  Social  Science,  which  ascertains  the  laws 
that  govern  men  when  combined  in  cities  and  nations. 

Each  of  these  departments  may  be  divided  into  many  branches,  as  Physics 
into  Acoustics,  Optics,  Electricity,  and  the  like ;  or  Social  Science  into  Morals, 

Politics,  Political  Economy,  Law,  and  the  like There  is  a 

general  correspondence  between  this  classification  and  the  order  in  which  the 
various  objects  of  science  came  into  being.  The  heavenly  bodies  were  first 
appointed  their  paths  in  the  celestial  spaces ;  then  the  surface  of  our  earth 
was  prepared  for  living  creatures ;  then  they  were  created  after  their  kind, 
and  man  the  last.  The  social  life  of  man  grew  up  last  of  all,  when  his  race 
was  multiplied  on  the  globe ;  and  ever  as  new  elements  appear,  the  conditions 
of  society  are  being  modified  even  to  the  present  time." 

We  are  now  in  a  position  to  sketch  the  table  of  the  Sciences. 

"CLASSIFICATION   OF  THE   SCIENCES. 
Group.  Mode  of  Treatment. 

1.  MATHEMATICS Theoretical.        Historical.         Applied. 

II.  ASTRONOMY "  "  " 

III.  PHYSICS ••  " 

IV.  CHEMISTRY "  "  " 

V.  PHYSIOLOGY "  •* 

VI.  ANTHROPOLOGY M  "  " 

VII.  SOCIAL  SCIENCE "  M  " 

RELIGIOUS  PHILOSOPHY." 

2.  The  Complete  Philosophy. —  Thinkers  have  also  aimed, 
in  dealing  with  the  question  "  Why?"  to  construct  the  uni- 
versal philosophic  system,  and  with  equally  various  success. 
The  common-sense  philosophy  may  be  accepted  as  the  best. 

The  philosopher  must  seek  to  give  a  rational  explanation  of  the  ul- 
timate facts  to  which  all  scientific  investigation  of  phenomena  leads. 
These  ultimate  facts  are  three :  consciousness ;  the  cosmos  of  matter 
and  spirit ;  the  being  back  of  all  on  which  all  depends.     A  complete 
18 


206  PRACTICAL   LOGIC. 

philosophy  must,  therefore,  have  its  psychological  theory,  its  cosmo- 
logical  theory,  and  its  ontological  theory.     The  three  are  embraced  in 

THE  COMMON-SENSE  PHILOSOPHY. 

I.  PSYCHOLOGICAL  THEORY.. ..Consciousness  is  made  up  of  two  ele- 
ments of  knowledge:  experience 
and  intuitioji. 

II.  COSMOLOGICAL  THEORY The  Cosmos  is  made  up  of  two  ele- 
ments: spirit  and  matter. 

III.  ONTOLOGICAL  THEORY The  Ultimate  Being,  or  First  Cause 

of  the  Cosmos,  is  the  infinite,  per- 
sonal Spirit,  God. 

Section  II,— Practical  Construction, 

Practical  construction  is  construction  according  to  the 
law  of  the  good.  Its  product  is  Practical  System. 

Topic  First. — Process  of  Forming  and  Verifying  Practical 
System. 

Three  things  are  essential  to  thinking  in  the  form  of  prac- 
tical construction :  First,  the  intelligent  fixing  upon  some 
one  complex  plan  or  aim ;  secondly,  the  careful  preparation 
or  gathering  of  ideas  and  forces  which  will  serve  as  means 
to  this  end;  thirdly,  the  best  arrangement  and  adjustment 
of  the  means  to  secure  the  end  in  view.  These  give  the 
laws  of  practical  aim,  practical  adaptation,  and  practical 
unity. 

I.  The  Law  of  Fraotical  Aim. 

Practical  aim  in  constructive  thinking  requires  that  the  view  be 
fixed  upon  some  beneficent,  useful,  rational,  or  moral  end  to  be  attained. 
Hence  arises 

Rule  1st.  —  Fix  upon  and  define  clearly  in  the  mind  the  end  to  be 
attained. 

II.  The  Law  of  Practical  Adaptation. 

Practical  adaptation  in  constructive  thinking  requires  that  all  the 
material  made  use  of  be  such,  and  only  such,  as  is  suited  to  secure  the 
proposed  end.  Hence  arises 


THE  UNFOLDING  OP  SYSTEMS.     207 

Rule  2d. —  See  that  the  suitable  means  are  provided  for  attaining 
the  proposed  end. 

III.  The  Law  of  Practical  Unity. 

Practical  unity  in  constructive  thinking  requires  that  all  the  means 
be  combined,  arranged,  and  adjusted  in  such  system  as  best  to  secure 
the  end  proposed.  Hence  arises 

Rule  3d. — See  that  the  means  are  properly  correlated  so  as  to 
secure  the  proposed  end. 

Topic  Second.  —  Products  of  Practical  Construction. 

The  Laws  of  Practical  Construction  govern  in  the  pro- 
duction of  all  inventions,  ideals,  plans  of  life,  etc.  Success 
in  life  depends  largely  upon  the  possession  of  this  power  in 
proper  development. 

One  of  the  highest  forms  of  practical  construction  is  found  in  oratory, 
in  which  the  aim  is  to  arrange  thought  in  such  a  system  as  shall  induce 
a  change  of  view,  of  judgment,  of  feeling,  or  of  purpose  in  an  audience. 

Illustrations  will  suggest  themselves  to  the  teacher  and  student. 
For  the  purpose  of  directing  in  the  work,  a  few  examples  will  suffice. 

Praxis.  —  Study  as  practical  systems:  1.  A  steam-engine.  2.  A 
telephone.  3.  A  plough.  4.  The  speech  of  Daniel  Webster,  in  the 
trial  of  John  Francis  Knapp,  for  the  murder  of  Joseph  White.  5. 
The  oration  of  Demosthenes  on  the  Crown. 


CHAPTER   II. 

THE  UNFOLDING  AND  TESTING-  OF  SYSTEMS. 

THE  best  use  of  the  power  of  construction  in  the  work  of 
thinking  requires  that  the  thinker  should  be  able  to  grasp 
and  unfold  what  may  be  contained  in  any  system,  and  to 
test  such  system  by  the  principles  of  construction,  scientific 
and  practical. 

For  the  purposes  of  the  brief  discussion  here  proposed,  the  two  forms 
of  logical  system  need  not  be  separated.  Two  things  are  of  prime 
importance:  first,  the  ascertaining  of  the  elements  of  systems,  and 
secondly,  the  testing  of  systems. 


208  PRACTICAL    LOGIC. 

Section  I,— Ascertaining  the  Elements, 
The  elements  of  any  system  may  be  learned  from  the 
Laws  of  Construction.  In  unfolding  scientific  constructions 
(to  which  attention  will  be  confined)  three  things  are 
embraced :  First,  the  grasping  of  the  totality  involved  in 
the  system ;  secondly,  the  study  of  the  relations  of  the  parts 
or  the  articulation  of  the  system ;  thirdly,  the  comparison 
of  the  system  with  the  objective  reality.  The  careful  study 
of  these  elements  is  requisite  to  prepare  for  the  testing  of 
systems. 

Topic  First. — The  Whole  and  its  Principle. 

In  studying  any  system  it  is  necessary  first  to  seize  upon 
it  as  a  whole  by  ascertaining  the  principle  which  unites  its 
elements. 

A  system  is  "  an  organized  body  of  truth,  or  truths  arranged  under 
one  and  the  same  idea,  which  idea  is  as  the  life  or  soul  which  assim- 
ilates all  those  truths."  In  studying  and  unfolding  any  system,  it  is, 
therefore,  necessary  to  inquire  first  for  this  organic  idea  or  principle, 
which  is  the  soul  of  the  system.  This  holds  in  all  three  forms  of  sys- 
tem, scientific,  aesthetic,  and  practical. 

Trendelenburg  distinguishes  "  systems  of  arrangement,"  correspond- 
ing to  systems  of  classes  (p.  47);  and  "systems  of  development," 
corresponding  to  the  products  of  scientific  construction  (p.  202). 
The  former  arise  under  Conception,  by  Classification  or  Division ;  the 
latter,  under  Reasoning,  by  Induction  and  Deduction.  The  former 
take  the  form  of  the  descriptive,  classificatory,  or  natural  history 
sciences,  —  as  Botany,  Zoology,  etc. ;  the  latter,  of  explanatory  natural 
and  mental  sciences,  —  as  Physics,  Chemistry,  Psychology,  etc. 

The  principle  or  organic  idea  in  systems  of  classes,  is  simply  the 
principle  of  classification  (p.  47)  or  division  (p.  68),  which  has  already 
been  considered.  E.  g.,  in  Zoology  the  system  of  the  animal  kingdom 
is  a  system  of  classes  and  sub-classes,  based  on  plan  of  organic  structure. 

The  principle  or  organic  idea  in  the  higher  form  of  system,  or  sys- 
tem in  the  stricter  sense,  is  the  central  truth  to  which  the  inductive 
method  leads,  and  with  which  the  deductive  method  starts  out. 

Accordingly,  Ueberweg  has  said :  "  The  principles  of  knowledge  are  of  two 
kinds,  according  as  the  individual  or  particular,  or  the  universal,  serves  as  the 


THE  UNFOLDING  OF  SYSTEMS.     209 

starting-point  of  knowledge.  The  former  do  not  correspond  to  the  real  prin- 
ciples, but  form  the  natural  foundations  of  propaedeutic  knowledge;  the 
latter  distinctly  correspond  to  real  principles  and,  accordingly,  form  the 
foundations  of  strictly  scientific  knowledge. 

"The  propaedeutic  or  method  of  investigation  proceeds  regressively  or 
analytically  to  the  knowledge  of  real  principles ;  the  purely  scientific  or  con- 
structive method  proceeds  progressively  or  synthetically  from  principles  to 
particulars  or  individuals.  But  it  is  by  no  means  always  desirable,  in  an 
exposition  of  the  sciences,  to  thoroughly  separate  the  analytic  from  the 
synthetic  elements.  Both  are  often  to  be  combined  with  each  other  in  the 
treatment  of  individual  problems." 

The  construction  and  value  of  a  system  will,  therefore,  manifestly  depend, 
in  any  given  case,  first  of  all,  upon  the  correctness  and  completeness  of  the 
principle  which  unites  its  parts  into  a  whole.  Hence,  in  examining  systems, 


Rule  1st.  —  Ascertain  the  principle  or  organic  idea  of  the  system. 

In  a  system  of  Ethics  the  idea  of  right  or  virtue  is  the  principle. 
In  the  Moral  System  of  the  universe  the  idea  of  right  as  embodied  in 
the  control  of  the  Moral  Governor  is  the  principle. 

Topic  Second. — The  Articulation  or  Relation  of  the  Parts. 

In  studying  any  system  it  is  necessary,  in  the  second  place, 
to  seize  upon  the  relations  of  the  parts  to  each  other. 

Every  truth  has  relation  to  some  other.  In  a  system  the  various 
connections  of  related  truths  are  brought  out.  Bishop  Butler  says, 
in  his  Sermons :  "  A  System,  Economy,  or  Constitution,  is  a  one  or  a 
whole,  made  up  of  several  parts,  but  yet  the  several  parts  even  con- 
sidered as  a  whole  do  not  complete  the  idea,  unless  in  the  notion  of  a 
whole  you  include  the  relations  and  respects  which  these  parts  have 
to  each  other." 

The  relations  of  the  thoughts  to  each  other,  in  any  system,  may  in- 
clude any  or  all  the  possible  relations  of  conception,  judgment  and 
reasoning.  The  aim  in  all  systematic  knowledge  is  "  to  unite  the  facts 
of  knowledge  so  as  to  see  them  in  their  several  bearings."  Hence 


Rule  2d. — See  that  the  parts  of  the  system  are  logically  connected 
throughout. 

Topic  Third. — The  Relation  to  the  Objective  Reality. 

In  studying  any  system,  it  is  necessary,  in  the  third 
place,  to  compare  the  thought-system  with  the  reality 
which  it  represents. 

18*  O 


210  PRACTICAL   LOGIC. 

"System  applies  not  only  to  our  knowledge,  but  to  the  objects  of 
our  knowledge.  Thus  we  speak  of  the  planetary  system,  the  muscu- 
lar system,  the  nervous  system.  We  believe  that  the  order  to  which  we 
would  reduce  our  ideas  has  a  foundation  in  the  nature  of  things.  And 
it  is  this  belief  that  encourages  us  to  reduce  our  knowledge  of  things 
into  systematic  order." 

The  final  test  of  the  correctness  of  any  system  must  be  found,  there- 
fore, in  its  exact  truthfulness.  Hence  arises 

Bule  3d.  —  See  that  the  system  agrees  exactly  with  the  reality. 

Section  II,— Testing  of  Systems. 

As  the  highest  process  in  the  formation  of  thought  is  the 
construction  of  systems,  so  the  highest  process  in  the  un- 
folding of  thought  is  the  testing  of  systems. 

The  possibilities  and  dangers  of  error  have  been  seen  to  be  very 
great  in  Conception,  Judgment  and  Reasoning,  but  they  must  evi- 
dently be  as  much  greater  in  Systematizing,  as  this  form  of  thought 
is  higher  and  more  difficult  than  the  others.  Mohammedanism  and 
Buddhism  in  religion,  Epicureanism  and  Utilitarianism  in  morals,  and 
numberless  other  systems  in  all  departments  of  thought,  maintain  their 
hold  upon  mankind  simply  because  of  the  inability  of  the  masses  of 
mankind  to  ascertain  their  elements  and  put  the  systems  themselves 
to  the  test. 

Some  examples  of  the  testing  of  systems  will  best  illustrate  the  kind 
of  work  to  be  done  in  order  to  avoid  error.  In  a  text-book  of  the 
scope  of  the  present,  it  is  impossible  to  find  space  for  presenting  such 
examples  in  detail.  The  work  must,  therefore,  be  confined  to  giving 
directions  for  testing  systems,  and  referring  the  teacher  and  student 
to  examples  of  such  testing  to  be  found  elsewhere. 

Topic  First, — Directions  for  Testing. 

The  first  inquiry,  resulting  from  the  carrying  out  of  Rule 
1st,  is,  What  is  the  organic  thought  or  principle  which  holds 
together  the  parts  of  the  system  ? 

The  second  inquiry,  resulting  from  Rule  2d,  is,  Are  the 
parts  logically  connected  ? 

The  third  inquiry,  resulting  from  Rule  3d,  is,  Does  the 
system  of  thought  agree  with  the  facts  or  the  reality  ? 


THE    UNFOLDING    OF  SYSTEMS.  211 

Archbishop  Whately  has  clearly  marked  out  the  course  to  be  pur- 
sued in  testing  a  system  of  argument.  We  quote  his  directions,  which 
are  as  follows : 

"  First,  then,  of  whatever  length  the  reasoning  may  be,  whether  treatise, 
chapter,  or  paragraph,  begin  with  the  concluding  assertion,— not  necessarily 
the  last  sentence  expressed,  but  the  last  point  established,— and  this,  whether 
it  be  formally  enunciated  or  left  to  be  understood.  Then,  tracing  the  reason 
backwards,  observe  on  what  ground  that  assertion  is  made.  The  assertion 
will  be  your  Conclusion ;  the  ground  on  which  it  rests  your  Premises.  The 
whole  Syllogism  thus  obtained  may  be  tried  by  the  rules  of  Logic. 

"  If  no  incorrectness  appear  in  this  syllogism,  proceed  to  take  the  premises 
separately,  and  pursue  with  each  the  same  plan  as  with  the  conclusion  you 
first  stated.  A  premise  must  have  been  used  as  such,  either  because  it  required 
no  proof,  or  because  it  had  been  proved.  If  it  have  not  been  proved,  consider 
whether  it  be  so  self-evident  as  to  have  needed  no  proof.  If  it  have  been 
proved,  you  must  regard  it  as  a  conclusion  derived  from  other  assertions 
which  are  premises  to  it,  so  that  the  process  with  which  you  set  out  will  be 
repeated,  viz.,  to  observe  on  what  grounds  the  assertion  rests,  to  state  these 
as  premises,  and  to  apply  the  proper  rules  to  the  syllogism  thus  obtained. 
Having  satisfied  yourself  of  the  correctness  of  this,  proceed,  as  before,  to  state 
its  premises,  if  needful,  as  conclusions  derived  from  other  assertions.  And 
thus  the  analysis  will  go  on  (if  the  whole  chain  of  argument  be  correct)  till 
you  arrive  at  the  premises  with  which  the  whole  commences,  which  of  course 
should  be  assertions  requiring  no  proof;  or,  if  the  chain  be  anywhere  faulty, 
the  analysis  will  proceed  till  you  come  to  some  proposition,  either  assumed  as 
self-evident  though  requiring  proof,  or  incorrectly  deduced  from  other  asser- 
tions." See  Whately's  Logic,  pp.  418,  419. 

Topic  Second. — Examples  Illustrative. 

The  teacher  of  Logic  will  be  able  to  furnish  illustrations 
of  this  subject  in  every  department  of  thought. 

I.  Familiar  Subjects. 

The  tests  should  be  applied  first  to  familiar  subjects. 
These  are  found  in  the  text-books  of  Arithmetic,  Geography, 
Physical  Geography,  Grammar,  Rhetoric,  Psychology,  Ethics, 
etc.,  used  in  the  study  of  these  various  departments. 

One  of  the  most  important  and  useful  of  all  mental  processes  is  that 
of  studying  and  grasping  a  science  in  its  entirety  as  a  system.  It 
trains  all  the  mental  faculties, — simple  cognition,  memory,  compar- 
ison and  construction.  Until  a  science  is  so  grasped,  it  is  not  in  any 
proper  sense  mastered,  since  the  main  thing  in  a  science  is  not  its  sep- 
arate facts  and  truths,  but  its  whole  of  related  facts  and  truths. 


212  PRACTICAL    LOGIC. 

The  best  preparation  for  grasping  and  testing  large  and  complex 
systems  of  thought  is  secured,  by  constantly  training  the  student  to 
analyze,  outline,  and  test  the  parts  and  chapters  of  the  text-books 
used. 

II,  More  Difficult  Subjects. 

The  logical  training  of  the  young  is  not,  however,  com- 
plete until  this  process  of  testing  has  been  extended  to  more 
difficult  and  abstruse  subjects.  The  following  illustrations 
of  such  testing,  found  in  various  works, — some  of  which  at 
least  will  be  within  the  reach  of  every  teacher  of  Logic, — 
may  be  of  service.  The  illustrations  may  be  extended  at 
pleasure  by  the  teacher. 

1.  Analysis  of  Part  First  of  Paley's  Evidences  of  Christianity.     See 
Whately's  Logic,  Appendix  III.,  pp.  421-427. 

2.  Mill's  Criticism  of  the  Theistic  Argument  for  a  First  Cause,  in 
Three  Essays  on  Religion.     Criticised  in  Princeton  Review,  September, 
1878,  Article  "John  Stuart  Mill  and  the  Destruction  of  Theism." 

3.  Herbert  Spencer's  First  Principles.     Criticised  in  The  Philosophy 
of  Herbert  Spencer,  by  Professor  Borden  P.  Bowne ;  and  in  Mr.  Spen- 
cer's Formula  of  Evolution,  by  Malcolm  Guthrie. 


GENERAL   SUMMARY. 

THE  last  aim  of  all  training  in  thinking  should  be  to  pre- 
pare for  and  lead  to  constructive  thinking.  The  safe  con- 
duct of  life,  in  the  largest  and  best  sense,  will  depend  upon 
the  thinker's  power  to  know  in  system, — that  is,  to  distin- 
guish between  true  systems  and  false  systems,  as  presented 
by  others,  and  to  construct  true  systems  scientific  and  prac- 
tical for  himself.  To  help  to  prepare  man  intellectually 
for  such  conduct  of  life  should  be  the  aim  of  the  Practical 
Logic  of  Construction. 


INDEX. 


Absolute,  terms  =  non-relative,  55 ; 
being,  28. 

Abstract,  or  abstract  notion,  31. 

Abstraction,  31. 

Accident,  separable  and  inseparable, 
29. 

Accidental  definition  =  description, 
76. 

Added  determinants,  126. 

Additions,  inference  by,  126. 

Adequate  knowledge,  91 ;  perfectly 
and  practically,  91. 

A  dicto  secundum  quid,  193. 

Affirmative  propositions  or  judg- 
ments, 111. 

Ambiguity,  of  terms,  82 ;  of  negative 
particles,  111;  of  all,  some,  etc.,  113; 
fallacy  from,  195 ;  sources  of,  82. 

Amphibology,  fallacy  of,  195. 

Ampliative  judgments,  99. 

Analogy,  137, 158. 

Analysis,  logical,  58;  two  kinds,  58. 

Analysis!  phyqiralt  32;  ™onfa^  ft2j_y 
^Analytic  judgment,  99. 

Antecedent,  117;  not  cause,  150. 

Argument,  as  middle  term  and  cause, 
138. 

Argumentum,  ad  ignorantiam,  181 ;  ad 
hominem,  181 ;  adjudicium,  181 ;  ad  ver- 
ecundiam,  181 ;  a  fortiori,  180. 

Argumentum  ex  concesso,  a  proof 
derived  from  a  proposition  already  con- 
ceded. 

Aristotle's  Dictum,  138. 

Art,  definition,  14. 

Artificial  Classification,  42,  65. 

Assertion  ==  a  statement  or  proposi- 
tion, affirmative  or  negative,  92. 

Association,  ambiguity  from,  82. 


Assumption,  any  proposition  taken 
for  granted  as  the  basis  of  an  argu- 
ment ;  unwarranted,  193. 

Attribute,  28  ;  term,  54 ;  proved,  177. 

Attributive,  term  =  connotative  term, 
54;  judgment,  113. 

Authority,  defined,  105;  competency 
of,  104 ;  credibility  of,  105 ;  concurrence 
of,  106. 

Axioms  of  Logic,  18. 

Baconian     Method,    or     inductive 

method,  148. 

Barbara,  Celarent,  etc.,  177. 
Base,  logical,  64. 
Begging  the  question,  193. 
Belief,  16 ;  see  Probability.    • 

Calculation  of  Probabilities,  181 ; 

overestimation  in,  193. 
Canons,  of  Inductive  Method,  149 ;  of 

syllogism,  170-175. 
Canons  of  Syllogism,  170. 
Categorematic  words,  54. 
Categorical,  propositions,  117;  syllo- 
gisms, 141 ;  syllogisms  tested,  162. 
Categories,  27 ;  Aristotle's,  30. 
Cause,  149,  86 ;  in  induction,  138 ;  test, 
153;  complex,  154;  hypothetical,  152. 

"Aristotle  distinguished  four  kinds 
of  causes  for  the  existence  of  a  thing. 
— 1.  The  Material  Cause,  the  sub- 
stance or  matter  composing  it;  2. 
The  Formal  Cause,  the  pattern,  type, 
or  design,  according  to  which  it  is 
shaped ;  3.  The  Efficient  Cause,  the 
force  employed  in  shaping  it ;  4.  The 
Final  Cause,  the  end,  motive,  or  pur- 
pose of  the  work." 

213 


214 


INDEX. 


Chain  syllogisms,  143. 

Chance,  definition,  181. 

Changes,  in  meaning  of  words,  82; 
periodic,  151. 

Characteristics  =  marks  or  proper- 
ties, 28. 

Circulus,  in  definiendo,  86 ;  inprobando, 
193. 

Classes,  single,  42  ;  systems  of,  42 ;  ex- 
tent of,  44 ;  relations  of,  44 ;  distinc- 
tions arising  from,  45. 

Classification,  process,  41 ;  rules,  42 ; 
results,  44;  special  relations  from,  45 ; 
artificial  and  natural,  65,  42. 

Clearness  of  knowledge,  90. 

Cognition  or  knowing,  10. 

Collective  terms,  53;  undistributed, 
113. 

Colligation,  definition  by,  79. 

Comparison,  faculty  of,  12 ;  of  objects, 
34;  of  notions  or  terms,  92;  of  judg- 
ments, 134;  by  similar  properties,  34. 

Compatible  terms,  55. 

Complex,  concept,  35 ;  proposition,  119 ; 
syllogism,  142. 

Complex  conceptions,  development 
of,  121. 

Composition  of  Causes,  in  complex 
cause,  154. 

Composition,  fallacy  of,  195. 

Compound,  proposition,  119;  syllo- 
gism, 142. 

Comprehension  of  terms,  39. 

Concept  proper,  37 ;  rules  for  form- 
ing, 37,  38;  distinctions,  39;  relation 
to  class,  47. 

Conception,  definition,  12,  25 ;  forma- 
tion of,  25  ;  unfolding  of,  56 ;  elements 
of,  26 ;  proper,  34 ;  products,  56 ;  logical 
quality,  90. 

Conclusion,  of  syllogism,  138;  false, 
141,  193 ;  weakened,  171 ;  from  plura- 
tive  judgments,  169;  principles  govern- 
ing, 166;  from  substitutive  judgments, 
170. 

Concrete  terms,  53. 

Concurrence,  of  testimony  and  au- 
thority, 106. 

Condition,  149. 

Conditional,  propositions  or  judg- 
ments, 47 ;  syllogisms,  145,  185. 

Confusion  of  words,  sources  of,  81. 

Connotation  of  terms,  54. 

Consequence  =  the  connection  be- 
tween the  antecedent  and  consequent. 


Consequent,  reason  and,  20 ;  fallacy  of 
the,  or  non  sequitur,  194 ;  in  conditional 
propositions,  117 ;  as  effect  of  cause,  20. 

Consilience  of  Inductions  =  "  the 
agreement  of  inductions  derived  from 
different  and  independent  series  of 
facts,  as  when  we  learn  the  motion  of 
the  earth  by  entirely  different  modes  of 
observation  and  reasoning."—  Whewell. 

Consistent  terms  =  compatible  terms. 

Conspectus,  of  relations  of  concepts, 
40 ;  of  relations  of  classes,  45 ;  of  judg- 
ments, 115;  of  grammatical  proposi- 
tions, 116 ;  of  opposing  judgments,  131 ; 
of  figures  of  syllogism,  163 ;  of  moods, 
176 ;  of  things  proved  by  the  figures, 
177 ;  of  valid  moods,  177 ;  of  fallacies, 
191. 

Construction,  Logic  of,  199-212. 

Content,  of  concepts  or  terms,  39. 

Contradiction,  law  of,  18;  of  judg- 
ments, 129. 

Contradictory,  terms,  55;  proposi- 
tions, 129;  opposition,  129. 

Convergent  evidence,  106. 

Converse  fallacy,  of  accident,  193. 

Conversion  of  propositions,  126; 
simple,  127 ;  by  limitation,  127 ;  by  con- 
traposition, 128;  by  opposition,  128. 

Convertend,  126. 

Coordinate,  conceptions,  44 ;  proposi- 
tions, 119. 

Copula,  94. 

Criterion  =  of  truth,  15. 

Cross  division,  69. 

Data,  the  facts  from  which  a  conclusion 
is  to  be  drawn,  147. 

Declaration,  75. 

Deduction  and  Induction,  136. 

Deductive  or  Combined  Method, 
203. 

De  facto  =  what  actually  or  really 
happens,  as  opposed  to  de  jure,  what 
ought  to  happen  by  law  or  right. 

Definition,  75 ;  rhetorical,  75 ;  etymo- 
logical and  by  word  analysis,  76 ;  loose, 
77 ;  logical,  75,  77  ;  perfect,  78;  of  class 
terms,  78;  of  attribute  terms,  78;  im- 
perfect, 79 ;  extended,  79 ;  nominal,  real 
and  genetic,  80 ;  rules,  81. 

Demonstrative  judgments,  131. 

Demonstrative,  or  absolutely  conclu- 
sive, proof,  analytic,  101;  intuitive, 
103;  indirect,  129. 


INDEX 


215 


Denomination,  or  naming,  49 ;  pro- 
cess and  modes,  49 ;  rules,  50 ;  products 
of,  52. 

Denotation  of  terms  =  extent,  44. 

Depth  of  a  notion  ;  see  Content. 

Description,  or  accidental  definition, 
76. 

Destructive  conditional  syllo- 
gism, 186. 

Diagrams,  of  content,  40 ;  of  extent, 
45;  of  opposition,  129;  of  syllogism, 
167-175. 

Dichotomy,  65. 

Differences  and  resemblances,  41. 

Differentia,  or  specific  difference,  46. 

Dilemma,  145;  rules  of,  189. 

Dilemmatic,  judgments,  118;  syllo- 
gisms, 145,  189. 

Discovery,  or  investigation,  method  of, 
209. 

Discursive  faculties,  11. 

Disjunction,  inference  by,  126. 

Disjunctive,  propositions,  117  ;  distin- 
guished from  partitive,  118 ;  converted, 
118;  syllogisms,  145,  188. 

Distinct  knowledge,  90. 

Distribution  of  terms,  111-113;  rules, 
115. 

Division,  logical,  57,  64 ;  principle  of, 
64;  forms,  65;  dichotomous,  66 ;  natu- 
ral, 67 ;  rules,  68. 

Divisions  of  Logic,  22;  principle  of, 
24. 

Doubt  =  hesitation  between  various 
views,  181. 

Empirical  judgments  and  proofs,  103. 

Enthymeme,  142. 

Epichirema,  142. 

Episyllogism,  142. 

Equivocal  terms,  82. 

Equivocation,  sources  of,  82 ;  fallacy 
of,  195. 

Essence,  29. 

Essential  propositions  —  explica- 
tive, 99. 

Euler's  Notation,  45. 

Evidence  =  any  facts  apprehended  by 
the  mind  and  made  the  grounds  of 
knowledge  and  belief.  As  testimony 
and  authority,  103;  convergent,  106. 

Exceptional  facts,  155. 

Excluded  middle,  law  of,  19. 

Exhaustive  division,  70. 

Experience,  16, 103, 147. 


Experimentum  crucis,  156. 

Experts,  definition,  104. 
Explanation    of  facts,  in  induction, 

148,  155. 

Explicative  propositions,  99. 
Extension,  or  extent,  44 ;  relations  of 

to  content,  48. 

Extensive  Syllogism,  163. 
Extremes,  or  terms,  of  a  proposition, 

52,94. 

Fact,  or  phenomenon,  148. 

Faculties,  of  intellect,  12,  72 ;  discur- 
sive, 13. 

Fallacies,  classification  of,  191 ;  in  in- 
duction, 159,  191 ;  in  deduction,  192 ; 
material,  193;  logical  or  formal,  194; 
semi-logical,  194. 

False  cause,  160, 192. 

Figures  of  speech,  in  definition,  87. 

Figures,  of  the  syllogism,  162 ;  canons 
of,  170. 

Forms  of  thought,  11. 

Fundamental  principle  of  syllo- 
gism, 138. 

Fundamentum  divisionis,  or  prin- 
ciple of  division,  68. 

General,  notion,  44 ;  term,  53. 

Generalization,  41  ;  as  product  of  in- 
duction, 157 ;  false,  159 ;  mere,  154. 

Genus,  46. 

Grammatical  combination  of  propo- 
sitions, 118. 

Grammatical  sentences,  116;  co- 
ordination of,  119;  subordination  of, 
119. 

Hamiltonian  Notation,  163. 

Hearsay,  definition  and  value,  104. 

Homonymous  terms,  83. 

Hypothesis,  finding  the  working,  147; 
testing,  153. 

Hypothetical,  propositions,  117;  syl- 
logisms, 144, 185. 

Identity,  law  of,  18 ;  of  concepts,  39. 
Ignoratio  Elenchi,  129,  193. 
Illative  Conversion,  126. 
Illicit  Process,  of  the  major  term,  of 

minor  term,  167. 
Immediate  inference,  134. 
Imperfect  figures,  of  the  syllogism, 

177. 
Imperfect  induction,  157. 


216 


INDEX. 


Inconsistent  propositions  =  con- 
tradictory, 129. 

Inconsistent  terms,  or  incompatible 
terms,  55. 

Indefinite  use  of  some,  114. 

Indirect  demonstration,  129. 

Indirect  reduction,  178. 

Individual,  46. 

Induction,  136;  unfolded,  147;  pro- 
ducts of,  157;  perfect  and  imperfect, 
158;  fallacies  in,  159, 191 ;  true,  156. 

Inductive  syllogism,  157 ;  guess,  156. 

Inference,  mediate  and  immediate,  134. 

Infima  species,  46. 

Infinitation,  judgments  from,  124. 

Inseparable  accident,  29. 

Instances,  exceptional,  155. 

Intellect,  faculties  of,  13,  72. 

Intension,  39. 

Intensive  syllogisms,  163. 

Intention,  first  and  second.  "  Of  the 
first  intention  are  the  names  of  things, 
a  man,  stone,  etc. ;  of  the  second  are  the 
names  of  names  and  species,  as  univer- 
sal, particular,  genus,  species,  syllogism, 
and  the  like."— Hdbbes.  Terms  of  the 
second  intention  express  the  mode  in 
which  the  mind  regards  or  classifies 
terms  of  the  first  intention. 

Intuitive  knowledge,  31. 

Inversions  restored  to  normal  form, 
95,  111. 

Irrelevant  conclusion,  193. 

Judgment,  definition,  12,  92;  forma- 
tion of  and  elements,  93 ;  primitive  and 
logical,  97 ;  of  extent  and  content,  97 ; 
impersonal,  98;  verification  or  proof, 
98;  analytic  and  synthetic,  99 ;  intui- 
tive and  empirical,  101 ;  products,  110 ; 
quality,  quantity,  relation,  and  modal- 
ity, 110;  normal  forms,  114;  categor- 
ical and  hypothetical,  117;  unfolding 
of,  121;  contained,  implied,  and  in- 
ferred, 121 ;  conversion  of,  126;  demon- 
strative, assertory,  and  problematic, 
131 ;  of  observation,  97. 

Language,  its  relation  to  thought,  50 ; 
ambiguities  of,  81 ;  in  definition,  85. 

Law,  149. 

Law  of  thought,  special  and  general, 
17;  fundamental,  18;  of  Identity,  18; 
of  Contradiction,  18 ;  of  Excluded  Mid- 
dle, 19 ;  of  Sufficient  Reason,  20. 


Limitation,  conversion  by,  127. 
Logic,  definitions,  8 ;  practical  aim,  13; 

postulates,  21 ;  divisions,  22. 
Lowest  species,  46. 

Major  term,  137;  premise,  138. 

Many  questions,  fallacy  of,  194. 

Material  fallacies,  193. 

Mediate  inference,  134. 

Members  of  division,  70. 

Metaphysical  division  =  Logical 
Partition,  57. 

Method,  logical,  23. 

Methods  of  indviction,  agreement, 
149;  difference,  150;  concomitant  vari- 
ations, 151 ;  residual  variations,  151. 

Metonymy  =  transfer  of  meaning,  82. 

Middle  term,  137. 

Minor  term,  137 ;  premise,  138. 

Miracles,  credible,  107. 

Mnemonic  verses,  177. 

Modal  propositions  =  those  assert- 
ing that  the  predicate  does  or  does  not 
belong  to  the  subject,  with  an  intima- 
tion of  the  mode  or  manner. 

Modality  of  judgments,  110,  131. 

Modus,  ponens,  186;  lollens,  186. 

Moods  of  the  syllogism,  164 ;  valid  and 
invalid,  176. 

Names  or  terms,  notative  and  symbol- 
ical, 50 ;  systems  of,  51 ;  positive  and 
non-positive,  abstract  and  concrete,  52 ; 
singular  and  universal,  53;  attribute 
and  class,  connotative  and  non-conno- 
tative,  simple  and  complex,  categore- 
matic  and  syn-categorematic,  54 ;  rela- 
tive and  non-relative,  compatible  and 
incompatible,  55 ;  univocal  and  equiv- 
ocal, 82 ;  homonymous,  83. 

Natural  Classification,  65,  42. 

Negation,  conversion  by,  128. 

Negative,  term,  52;  definition,  87; 
judgment,  111 ;  copula,  111 ;  premises, 
168 ;  conclusion,  166 ;  testimony,  104. 

Nominal  definition,  80. 

Non  causa  pro  causa,  192. 

Non  sequitur,  194. 

Notion,  39 ;  simple,  31 ;  identical  and 
different,  congruent  and  conflictive, 
contrary  and  contradictory,  39 ;  con- 
tent of.  39. 

Novum  Organum,  aim  of,  148. 

Numerically  definite,  judgment, 
114;  syllogism,  169. 


INDEX. 


217 


Object,  28. 

Objective,  28. 

Obscure  knowledge,  91. 

Observation,  definition,  26,  148;  dis- 
tinguished from  experiment,  148 ;  in- 
struments and  forms  of,  26  ;  objects  of, 
27  ;  processes  and  products,  31 ;  exact, 
32 ;  rules,  33. 

Occasion,  of  an  event  =  condition, 
149. 

Occult  forms  of  syllogism,  143. 

Opposite  terms  =  different  or  con- 
flictive,39. 

Opposition  of  propositions,  inference 
by,  128. 

Paralogism  =»  purely  logical  fallacy, 
191, 194. 

Parity  of  reasoning,  used  to  denote 
that  when  one  case  has  been  demon- 
strated, other  similar  cases  can  be  dem- 
onstrated by  a  like  course  of  reason- 
ing. 

Particular  premises,  168 ;  fallacy  of, 
194. 

Particular  propositions,  113. 

Partition  =  metaphysical  division, 
57. 

Partition,  logical,  57;  matter  of,  57; 
forms,  59 ;  rules,  60 ;  physical,  31. 

Partitive  judgments,  118. 

Per  accidens,  conversion,  127. 

Percept,  31. 

Perfect  figure,  of  the  syllogism  = 
Figure  I.,  177. 

Perfect  knowledge,  by  conception, 
90 ;  by  judgment,  131 ;  by  reasoning, 
198 ;  by  construction,  212. 

Periodic  changes,  151. 

Petitio  principii,  193. 

Phenomenon,  148. 

Philosophy,  definition,  204  ;  complete, 
205. 

Physical  definition  =  statement  of 
physical  parts. 

Plurative  propositions,  114;  syllo- 
gisms, 169. 

Polysyllogism,  142. 

Polytomy,  68. 

Porphyry,  tree  of,  66. 

Positive  terms,  52. 

Post  hoc,  ergo  propter  hoc,  192. 

Postulates  of  Logic,  21. 

Predicables,  27;    scheme  of,  30;  use 
of,  30 ;  observation  of,  30. 
19 


Predicaments  =  Categories. 

Predicate,  quantified,  164. 

Premise  in  reasoning,  138. 

Principle,  of  division,  64 ;  of  system, 
208. 

Privative  conception,  inference  by, 
124. 

Privative,  terms,  52. 

Probability,  degrees  of,  108 ;  the  guide 
of  life,  108 ;  calculation  of,  181 ;  in  in- 
duction, 158;  overestimation  and  un- 
derestimation of,  193. 

Problem  =*  an  assertion  put  forward  for 
proof  or  dis-proof. 

Proof  of  judgment,  98 ;  analytic,  100 ; 
synthetic,  101;  intuitive,  101;  empir- 
ical, 103 ;  from  testimony  and  authori- 
ty, 103. 

Proper  names,  53. 

Property,  definition,  28;  kinds,  27; 
distinguished  from  attribute,  quality, 
etc.,  28 ;  intrinsic  and  extrinsic,  28 ;  es- 
sential and  non-essential,  28 ;  peculiar, 
29;  accidental,  29. 

Propositions,  or  judgments,  classifica- 
tion of,  by  quality,  111;  by  quantity, 
112 ;  by  relation,  116 ;  by  modality,  131 ; 
by  grammatical  form,  118 ;  by  source 
of  predicate,  99. 

Prosyllogism,  142. 

Proximate  genus,  47. 

Quantification  of  predicate,  164. 
Quantity  of  propositions,  112. 
Quaternio  termiiiorum,  166, 194. 

Ratiocination  =»  Syllogism  or  Deduc- 
tion. 

Reason  =  middle  term,  139 ;  lazy  and 
controlling,  192. 

Reason  and  Consequent,  principle 
of,  20 ;  forms  of,  20. 

Reasoning,  logic  of,  134-198. 

Reductio,  ad  absurdum,  129,  181 ;  ad 
impossible,  178. 

Reduction,  of  figures,  177;  of  con- 
junctive syllogisms,  187. 

Relation  =  any  connection  in  thought 
or  fact  between  things.  Category  or 
properties  of,  27. 

Relative  terms,  55. 

Residues,  method  of,  151. 

Rules,  of  observation,  33  ;  of  concept- 
forming,  37 ;  of  classification,  42 ;  of 
naming,  50 ;  of  partition,  60 ;  of  divi- 


218 


INDEX. 


sion,  68 ;  of  definition,  81 ;  of  intuition, 
102;  of  testimony  and  authority,  104; 
of  obversion,  124 ;  of  illative  conver- 
sion, 126 ;  of  illative  opposition,  129 ;  of 
verifying  deduction,  139 ;  of  induction, 
148;  of  hypothesis,  153;  of  categorical 
syllogism,  166 ;  of  sorites,  179 ;  of  cal- 
culating probabilities,  182 ;  of  condi- 
tional syllogism,  186;  of  disjunctive 
syllogism,  188 ;  of  forming  system,  201 ; 
of  testing  system,  209. 

Science,  definition,  13,  204 ;  complete, 
204;  practical,  14. 

Semilogical  fallacies,  194. 

Sentence,  grammatical  forms,  118. 

Separable  accident,  29. 

Signs  of  judgments,  universal,  113; 
particular,  113 ;  approximately  univer- 
sal, 114. 

Similars,  grasped  in  conception,  35. 

Simple,  apprehension,  31 ;  conversion, 
127. 

Singular,  terms,  53 ;  judgments,  113. 

Sophism,  191. 

Sorites,  or  chain  syllogism,  143;  classi- 
fied, 144;  tested,  179. 

Specialization,  or  deduction,  136. 

Species,  in  Logic,  46 ;  in  Natural  His- 
tory, 46  ;  distinctions  of,  46-48. 

Subaltern,  genera  and  species,  46; 
propositions,  129. 

Subalternans,  subalternates,  129. 

Subcontrary,  129. 

Subject,  28;  and  predicate,  94;  naked, 
127. 

Subjective,  28. 

Subordinate,  genera  and  species,  47 ; 
propositions,  129. 

Substance,  definition,  28;  properties 
of,  28. 

Subsumption  =  bringing  a  special  case 
under  the  general  rule  or  law  ex- 
pressed in  the  major  premise  or  sump- 
tion, 192. 


Sufficient  Reason,  law  of,  20;  basis 

of  reasoning,  138. 
Summum  genus,  46. 
Sumption  =  major  premise,  192. 
Syllogism,  24,  134  ;  inductive,  157. 
Symbolical  terms,  50. 
Syncategorematic  terms,  54. 
Synthesis,  or  synthetic  method,  209. 
Synthetic  syllogism,  134. 
System,  definition  and  forms,  12,  199 ; 

of  classes,  46  ;  natural,  67. 

Tacit  or  occult  premise,  142. 
Tautology,  in  definition,  86. 
Terms,   or   names,   formation    of,  52; 

classification  of,  52-56 ;  distribution  of, 

115. 
Testimony  and  Authority,  nature 

of,  16 ;  proof  from  and  rules  for,  103. 
Theory  =  verified  hypothesis,  148. 
Thing,  32. 
Thought,  definition,  10 ;  forms,  11 ;  law, 

17. 

Transfer  of  meaning  of  terms,  82. 
Tree  of  Porphyry,  66. 
Trichotomy,  68. 
Trilemma=dilemmatic  syllogism  (145) 

with  three  alternatives. 
Truth,    definition   and   criterion,   15; 

modes  of  arriving  at,  16;  degrees  in 

assurance  of,  16. 

Universal,  terms,  53;  propositions,  112. 
Univocal  terms,  82. 

Variations,  method  of,  151 ;  periodic, 
151. 

Weakened  conclusion,  171. 

Weaker  part,  in  syllogism,  168. 

Whole,  kinds  of,  57. 

Witnesses,  competency,  104;  credibil- 
ity, 105;  concurrence  of,  106;  inci- 
dental variations  of,  106;  noted  liars, 
106. 


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